Looking at the Kepler pentagonal tiling, you may notice the nice looking rings of pentagons around the decagons.You can also make up other tilings with these rings of pentagons  to get the one below to work you have to sneak in some dented or overlapping pentagons.But which regular ngons can form rings like this? You obviously can't do it with a square.And some regular ngons, like heptagons, nonagons, decagons, and hendecagons (11gons) don't work either.All the angles of the regular ngon are (n2)pi/n  so the angles of the polygon in the center would have to be 4pi/n, but for that…
Math

Most Topular Stories

regular polygons, in rings
mathrecreation20 Jul 2015  9:01 pm 
How to Get to the Fourth Dimension
Scientific American  Math31 Jul 2015  6:30 amA new book offers mathematical puzzles, such as fitting a coin through a hole that seems too small to accommodate it  Read more on ScientificAmerican.com 
Math Mammoth Grade 7 (prealgebra)
Homeschool Math Blog25 Jun 2015  2:06 pmMath Mammoth Grade 7 and 7B are available now  as downloads! Printed books and a CD version will follow soon. Check www.mathmammoth.com/complete/grade_7.php for description and samples. 
Jun 17, Exponents rules
Mathforallgrades Blog17 Jun 2015  12:22 amExponents rules enable arithmetic expression of base and index. 
Median = Geometric Mean? A Common Core Investigation
MathNotations18 Jul 2015  4:12 pmAs tweeted on twitter.com/dmarain... J noticed that for an arithmetic sequence like 3,7,11,15,19 the median equals the arithmetic mean. In this case, the median and "mean" are both 11. She found this was wellknown and not too difficult to prove. She wondered if there was an analogous rule for geometric sequences like 2,4,8,16,32. Instead of the arithmetic mean she tried the geometric mean: (2•4•8•16•32)^(1/5) which equals 8, the median. VERIFY THIS WITHOUT A CALCULATOR! Unfortunately her conjecture failed for a geometric sequence with an even number of terms like 2,4,8,16…

MATH  Google News

New York City Questions English, Math and Science Taught at Yeshivas  New York Times
31 Jul 2015  7:17 pmNew York TimesNew York City Questions English, Math and Science Taught at YeshivasNew York TimesThe New York City Department of Education plans to investigate whether roughly three dozen private yeshivas are providing an adequate education in secular subjects like English, math and science, in response to a letter from parents, former students 
Algebra Camp boosts math skills for 300plus incoming ninthgraders  Your Houston News
31 Jul 2015  5:48 pmYour Houston NewsAlgebra Camp boosts math skills for 300plus incoming ninthgradersYour Houston News“The Algebra camp helped to excite students about math before they enter ninth grade,” said Yolonda Sneed, Jersey Village camp director. “Students are exposed to a rigorous high school curriculum while having fun without any grade penalties. Students ... 
Statesville Middle summer camp focused on science, math  Statesville Record & Landmark
31 Jul 2015  5:15 pmStatesville Record & LandmarkStatesville Middle summer camp focused on science, mathStatesville Record & Landmark... headstart this summer. For the past three weeks, about two dozen students discovered different ecosystems around creeks, planted and maintained vegetables, used math to create birdhouses and constructed boats with aluminum and swimming noodles.and more » 
Barbie's Bungee Jump Adventure Illustrates Math Concepts  KFYRTV
31 Jul 2015  4:30 pmKFYRTVBarbie's Bungee Jump Adventure Illustrates Math ConceptsKFYRTVThere's often a disconnect when trying to teach students how math and science applies in the real world. Teachers from around the state are in Bismarck to learn new and fun techniques. For most adults, Barbies are just a childhood memory. For North ...and more » 
Tuscaloosa City Schools holds job fair for math teachers  FOX6 WBRC  MyFoxAL.com
31 Jul 2015  4:02 pmTuscaloosa City Schools holds job fair for math teachersFOX6 WBRC  MyFoxAL.comTuscaloosa City Schools held an invitationonly job fair for highly qualified math teachers on Friday morning. School starts in two weeks and they have five openings that need to be filled. Administrators say there are about 100 openings statewide for and more »

Search for "math OR mathematics"

Former teacher pleads guilty to child seduction
31 Jul 2015  9:41 pmA former New Haven High School math teacher pleaded guilty Friday to one count of child seduction, a Level 5 felony, and one count of dissemination of harmful material, a Level 6 felony. Four other charges were dismissed. 
Lehrman has seen four decades of ACAC's best
31 Jul 2015  9:40 pmFor the last four decades, the Allen County Athletic Conference has been led by football coaching giants. Rick Minnich , Bob Yager , Kirk Sorg , Mark Lefebvre , Leland Etzler and then Jared Sauder built an identity of tough, hardhitting football for the league. 
Teachers Are Not Stressed, Underpaid
31 Jul 2015  9:39 pmI am responding to the July 19, 2015, article written by Marshall Greenstein regarding teacher stress and salaries. 
Stamford help exchange
31 Jul 2015  9:23 pmTo submit an item to Help Exchange, email localnews@scni.com with "Help Exchange" in the subject line. For more information, contact the Volunteer Center of United Way of Western Connecticut at 2033487714 unless otherwise noted. 
Breathtaking photos capture rare blue moon
31 Jul 2015  9:20 pmFriday night's blue moon wasn't blue, but its grandeur still prompted many to look up to the night sky in awe. People from all over the world gawked at the lunar rarity.

Mathematics News  ScienceDaily

Ants in the lead: How ants cooperate in steering food to their nest
30 Jul 2015  7:45 amA physicsbased model can explain how ants cooperate in steering food to their nest. To lug a large object, a number of ants surround it  the back ones lift, those on the leading edge pull. How do they stay on track, instead of simply pulling all around in a sort of tugofwar? Scientists used video analysis to track the individual movements of ants in a group that was carrying a large food item toward their nest. 
Majority rule: Why conformity can actually be a good thing
28 Jul 2015  9:57 amLike to go your own way? Most of us actually prefer to follow the pack, according to research. That's one of the outcomes from a study that examines how mathematical models predict human behavior. 
A new litmus test for chaos?
28 Jul 2015  8:07 amResearchers have come up with a new definition of chaos that applies more broadly than Lyapunov exponents and other previous definitions of chaos. The new definition fits on a few lines, can be easily approximated by numerical methods, and works for a wide variety of chaotic systems. 
The algorithm of writing
24 Jul 2015  12:19 pmResearchers explores the promise and peril of computerbased writing assessment software. 
Model for robots with bacteriacontrolled brains
16 Jul 2015  6:15 amA scientist used a mathematical model to demonstrate that bacteria can control the behavior of an inanimate device like a robot.

Scientific American  Math

How to Get to the Fourth Dimension
31 Jul 2015  6:30 amA new book offers mathematical puzzles, such as fitting a coin through a hole that seems too small to accommodate it  Read more on ScientificAmerican.com 
The World's Most Accurate Parquet Floor–Based Personality Test
24 Jul 2015  9:30 amAre you a neurotic loner or a charismatic cult leader? Try this highly scientific personality test based on a parquet floor from one of Antoni Gaudí's Modernista masterpieces to find out  Read more on ScientificAmerican.com 
What It Feels like to Be Cedric Villani
8 Jul 2015  1:00 pmThe Fields Medalist's memoir gives us a glimpse into the emotional highs and lows of being a passionate mathematician.  Read more on ScientificAmerican.com 
Researchers Race to Rescue the Enormous Theorem before Its Giant Proof Vanishes
8 Jul 2015  5:30 amBefore they die, aging mathematicians are racing to save the Enormous Theorem's proof, all 15,000 pages of it, which divides existence four ways  Read more on ScientificAmerican.com 
Back Algorithmic Knitting on Kickstarter
3 Jul 2015  7:00 amFabienne Serriere wants to hack an industrial knitting machine to make cellular automata scarves, and you can back her project on Kickstarter.  Read more on ScientificAmerican.com

NYT > Mathematics

The Singular Mind of Terry Tao
25 Jul 2015  9:00 pmA prodigy grows up to become one of the greatest mathematicians in the world. 
The Short Stories We Tell Ourselves About Everyday Spending
28 Jun 2015  9:00 pmPeople love to blur the numbers, even with everyday subjects like credit card spending. 
Meet the New Common Core
15 Jun 2015  9:00 pmBut don’t get too excited. It’s the same as the old one. 
‘How to Bake Pi,’ by Eugenia Cheng
13 Jun 2015  9:00 pmRecipes for tapping the logic and beauty of mathematics. 
Bedtime Math’s Founder Uses an Eggbeater for More Than Just Eggs
26 May 2015  9:00 pmLaura Overdeck turns an eggbeater into a teachable moment.

Loren on the Art of MATLAB

Incremental Delaunay Construction
15 Jul 2015  11:47 amI'm happy to welcome back Damian Sheehy as guest blogger. Last time Damian wrote about how Natural Neighbor interpolation addresses FAQs in scattered data interpolation. In this blog he will answer a FAQ on adaptively editing a Delaunay triangulation.ContentsIs delaunayTriangulation More Efficient than delaunay?When is Incremental Delaunay Important?Performance Example of Incremental Delaunay ConstructionYour Need for Geometric Tools?Is delaunayTriangulation More Efficient than delaunay?A technical support question that occasionally crops up asks about the best and most efficient way to… 
Natural Neighbor – A Superb Interpolation Method
1 Jul 2015  11:46 amI'm happy to welcome Damian Sheehy as this week's guest blogger. Damian works on the development of geometryrelated features at MathWorks. He will provide answers to two frequently asked questions; one on scattered data interpolation that he will cover in this blog and the other on Delaunay triangulation that he will cover in the next. Over to you, Damian...ContentsAn Email from Customer SupportWhy griddata or scatteredInterpolant May Be InconsistentExample of Inconsistent Behavior in Linear InterpolationWhy Natural Neighbor Interpolation is SuperiorYou Tell Me!An Email from Customer… 
How Do You Modify the Background of an Image?
24 Jun 2015  8:36 amToday I'd like to introduce guest blogger Brett Shoelson. Some of you may know Brett through his File Exchange submissions, or through his involvement with the Pick of the Week blog, or from occasional guest posts on Steve’s blog on image processing.Contents"The visa problem"The original photoFirst question: how do we isolate the background?Is the effort of automation justified?Improving the maskModifying the backgroundTwo problems remain...Planewise manipulationsFixing the interfaceA final note"The visa problem"Loren recently told me she had a pending international trip that requires a… 
Getting Started with Kaggle Data Science Competitions
18 Jun 2015  11:44 amHave you been interested in data science competitions, but not sure where to begin? Today's guest blogger, Toshi Takeuchi, would like to give a quick tutorial on how to get started with Kaggle using MATLAB.ContentsThe Titanic Competition on KaggleData Import and PreviewEstablishing the BaselineBack to Examining the DataExploratory Data Analysis and VisualizationFeature EngineeringYour Secret Weapon  Classification LearnerRandom Forest and Boosted TreesModel EvaluationCreate a Submission FileConclusion  Let's Give It a TryThe Titanic Competition on KaggleMATLAB is no stranger to competition… 
Advice for Making Prettier Plots
11 Jun 2015  6:27 amA few years ago, Jiro wrote a popular post for making pretty plots on this blog. We also host a blog specifically about graphics by Mike. And with the R2014b release of MATLAB came an updated graphics system that Dave described last year in a 3 part series: Part 1, Part 2, and Part 3.Even with that, I continue to hear questions about how to accomplish certain tasks, such as using a symbol to indicate degrees. This post contains a collection of a few tips that may help you update your plots to match more closely what you are trying to convey.ContentsPlotting Temperature DataAdd Y Label with…

Homeschool Math Blog

Math video for kids: Adding three numbers
8 Jul 2015  1:23 pmLet your little ones have fun learning how to add three numbers with this new video of mine, which also features Mathy the Mammoth as my mascot. :)The video is intended for first grade. 
Math Mammoth Grade 7 (prealgebra)
25 Jun 2015  2:06 pmMath Mammoth Grade 7 and 7B are available now  as downloads! Printed books and a CD version will follow soon. Check www.mathmammoth.com/complete/grade_7.php for description and samples. 
Homeschooling  history and state today
16 Jun 2015  3:19 pmHere's an interesting infographic about homeschooling  its history and its state today. Click to enlarge. :) Source: EarlyChildhoodEducationDegrees.com 
Homeschooling With Greater Joy and Peace
11 Jun 2015  12:55 pmThis is a guest post by Alecia Baptiste.Some days homeschooling our children can be amazing. We wake up in the morning feeling rested, excited about facing the challenges of the new day and eager to explore with our children. On those days our children are excited about learning and cooperative. And don't you love it when your children have those “Aha” moments? When they finally get that math concept or they make some connection between facts or after months of struggling to read, you see them lying contently in bed reading a book. On those day we think to… 
Math Mammoth printed versions in color
4 Jun 2015  6:05 amDid you know? Math Mammoth grades 13 printed books are now available as color versions through Rainbow Resource.Currently you need to access them via their search function: search for "math mammoth color". Hopefully they'll get their own category page soon.

Let's Play Math!

Math(s) Teachers at Play #88 via mathematicsandcoding
30 Jul 2015  11:20 amFrom elementary to high school, manipulatives to Minecraft, there’s plenty of fun to be had at this month’s math education blog carnival: Math(s) Teachers at Play 88 Enjoy! So, here is issue 88 of the Math(s) Teachers at Play blog carnival. This acts as a round up of some cool blog posts that have been published since issue 87 over at cavmaths. As usual people have submitted entries, which I will supplement with some posts that I have really enjoyed reading in the last few weeks. Click here to read the blog carnival post at mathematicsandcoding. [Feature photo (top) by Pratham… 
Noticing Fractions in a Sidewalk
28 Jul 2015  5:04 amMy daughters didn’t want to admit to knowing me, when I stopped to take a picture of the sidewalk along a back street during our trip to Jeju. But aren’t those some wonderful fractions? What do you see? What do you wonder? Here is one of the relationships I noticed in the outer ring: And this one’s a little trickier: Can you find it in the picture? Each square of the sidewalk is made from four smaller tiles, about 25 cm square, cut from lava rock. Some of the sidewalk tiles are cut from mostlysmooth rock, some bubbly, and some halfnhalf. I wonder how far we could go… 
Murphy Strikes My Paperbacks :(
23 Jul 2015  5:55 pmThe colors are supposed to go all the way off the edge. They worked just fine in the prepublication proof…Murphy’s Law struck today, and the paperback books that looked so good in the proof copies turned out to have a cover glitch, at least in the ones I ordered from Amazon. I’m working with CreateSpace to make sure it gets straightened out—but that means the books may show up as “unavailable” for awhile. As with any printondemand glitch, if you got a badly printed book you can ask Customer Support to replace it. It could be worse. The interior of the… 
30% Discount for Email Newsletter Subscribers
21 Jul 2015  12:41 am[Feature photo (above) by Glen Wright via Flickr (CC BY 2.0).] Wouldn’t it be wonderful if math was something your children WANTED to do? With the Math You Can Play series, your kids can practice their math skills by playing games with basic items you already have around the house, such as playing cards and dice. Paperback editions of the first two Math You Can Play books will be out any day now. If you’re subscribed to my Tabletop Academy Press Updates email newsletter, I’ll be sending you a 30% discount code by Thursday, or as soon as both books pass through the last few… 
Education Bloggers: Share Your Post!
20 Jul 2015  4:48 amphoto by Omar Omar via flickr If you are a homeschooler or classroom teacher, student or independent learner, or anyone else who writes about math, now is the time to send in your favorite blog post for next week’s Math Teachers at Play (MTaP) math education blog carnival. Click here to submit your blog post. Don’t procrastinate: The deadline for entries is this Friday, July 24. The carnival will be posted next week at mathematicsandcoding. If you haven’t written anything about math lately, here are some ideas to get your creative juices flowing… Need an IdeaStarter?

Computational Complexity

Explain this Scenario in Jeapardy and some more thoughts
28 Jul 2015  8:44 pmIn the last post I had the following scenario: Larry, Moe, and Curly are on Jeopardy. Going into Final Jeopardy: Larry has $50,000, Moe has $10,000, Curly has $10,000 Larry bets $29,999, Moe bets $10,000, Curly bets $10,000 These bets are ALL RATIONAL and ALL MATTER independent of what the category is. For example, these bets make sense whether the category is THE THREE STOOGES or CIRCUIT LOWER BOUNDS. Explain why this is. EXPLANATION: You were probably thinking of ordinary Jeopardy where the winner gets whatever he gets, and the losers takehome is based ONLY on their rank (2000 for second… 
Explain this Scenario on Jeopardy
27 Jul 2015  3:22 pmPonder the following: Larry, Moe, and Curly are on Jeopardy. Going into Final Jeopardy: Larry has $50,000, Moe has $10,000, Curly has $10,000 Larry bets $29,999, Moe bets $10,000, Curly bets $10,000 These bets are ALL RATIONAL and ALL MATTER independent of what the category is. For example, these bets make sense whether the category is THE THREE STOOGES or CIRCUIT LOWER BOUNDS. Explain why this is. I'll answer in my next post or in the comments of this one depending on... not sure what it depends on. 
New Proof of the Isolation Lemma
23 Jul 2015  6:07 amThe isolation lemma of Mulmuley, Vazirani and Vazirani says that if we take random weights for elements in a set system, with high probability there will be a unique set of minimum weight. Mulmuley et al. use the isolation lemma to randomly reduce matching to computing the determinant. The isolation lemma also gives an alternative proof to ValiantVazirani that show how to randomly reduce NPcomplete problems to ones with a unique solution. Noam TaShma, an Israeli high school student (and son of Amnon), recently posted a new proof of the isolation lemma. The MVV proof is not particularly… 
Hartley Rogers, Author of the first Textbook on Recursion Theory, passes away
21 Jul 2015  10:53 amHartley Rogers Jr passed away on July 17, 2015 (last week Friday as I write this).He was 89 and passed peacefully. For our community Rogers is probably best known for his textbook on Recursion Theory which I discuss below. He did many other things, for which I refer you to his Wikipedia page here. His book was: The theory of recursive functions and effective computability. It was first published in 1967 but a paperback version came out in 1987. It was probably the first textbook in recursion theory. It was fairly broad. Here are the chapter headings and some comments. Recursive functions… 
Microsoft Faculty Summit
16 Jul 2015  5:40 amLast week I participated in my first Microsoft Faculty Summit, an annual soiree where Microsoft brings about a hundred faculty to Redmond to see the latest in Microsoft Research. I love these kinds of meetings because I enjoy getting the chance to talk to computer scientists across the broad spectrum of research. Unlike other field, CS hasn't had a true annual meeting since the 80's so it takes events like this to bring subareas together. "Unlike other fields" is an expression we say far too often in computer science. This was the first summit since the closing of the Silicon Valley lab and…

Mathematics and Computation

Intermediate truth values
30 Jul 2015  1:16 amI have not written a blog post in a while, so I decided to write up a short observation about truth values in intuitionistic logic which sometimes seems a bit puzzling. Let $\Omega$ be the set of truth values (in Coq this would be the setoid whose underlying type is $\mathsf{Prop}$ and equality is equivalence $\leftrightarrow$, while in HoTT it is the hpropostions). Call a truth value $p : \Omega$ intermediate if it is neither true nor false, i.e., $p \neq \bot$ and $p \neq \top$. Such a “third” truth value $p$ is proscribed by excluded middle. The puzzle is to explain how the… 
The troublesome reflection rule (TYPES 2015 slides)
19 May 2015  8:10 amHere are the slides of my TYPES 2015 talk “The troublesome reflection rule” with fairly detailed presenter notes. The meeting is taking place in Tallinn, Estonia – a very cool country in many senses (it’s not quite spring yet even though we’re in the second half of May, and it’s the country that gave us Skype). Download slides: The troublesome reflection rule (TYPES 2015) [PDF]. 
Another PhD position in Ljubljana
3 Apr 2015  4:12 amIt is my pleasure to announce a second PhD position in Ljubljana! A position is available for a PhD student at the University of Ljubljana in the general research area of modelling and reasoning about computational effects. The precise topic is somewhat flexible, and will be decided in discussion with the student. The PhD will be supervised by Alex Simpson who is Professor of Computer Science at the Faculty of Mathematics and Physics. The position will be funded by the Effmath project (see project description). Full tuition & stipend will be provided. The candidate should have a… 
A HoTT PhD position in Ljubljana
22 Nov 2014  4:16 amI am looking for a PhD student in mathematics. Full tuition & stipend will be provided for a period of three years, which is also the official length of the programme. The topic of research is somewhat flexible and varies from constructive models of homotopy type theory to development of a programming language for a proof assistant based on dependent type theory, see the short summary of the Effmath project for a more detailed description. The candidate should have as many of the following desiderata as possible, and at the very least a master’s degree (or an equivalent one): a… 
TEDx “Zeroes”
16 Oct 2014  12:01 amI spoke at TEDx University of Ljubljana. The topic was how programming influences various aspects of life. I showed the audence how a bit of simple programming can reveal the beauty of mathematics. Taking John Baez’s The Bauty of Roots as an inspiration, I drew a very large image (20000 by 17500 pixels) of all roots of all polynomials of degree at most 26 whose coefficients are $1$ or $1$. That’s 268.435.452 polynomials and 6.979.321.752 roots. It is two degrees more than Sam Derbyshire’s image, so consider the race to be on! Who can give me 30 degrees? The code…

IMA Journal of Applied Mathematics  current issue

Travelling wave solutions in periodic monostable equations on a twodimensional spatial lattice
15 Jul 2015  8:48 amThis paper is concerned with travelling wave solutions of periodic monostable differential equations on a twodimensional lattice. The existence, stability and uniqueness of supercritical travelling wave solutions are obtained by comparison principle. 
Linear complementarity representation of piecewise linear functions
15 Jul 2015  8:48 amWe investigate a representation of piecewise linear function containing a complementarity condition, and call it a linear complementarity representation. This representation is also known as ‘Bokh1’ or ‘statevariable representation’ in literature. We discuss two spacial types of representation, called Prepresentation and ULTrepresentation, and give an elementary proof to show that either one of these two types of representation completely characterizes any piecewise linear function. We can also demonstrate that a Prepresentation can be transformed into a… 
Lowfrequency onsite identification of a highly conductive body buried in Earth from a model ellipsoid
15 Jul 2015  8:48 amIdentification of a highly conductive orebody buried in Earth using an equivalent, perfectly conducting, triaxial model ellipsoid is investigated. The real data available (threecomponent magnetic fields collected along a borehole due to a singlefrequency current loop at the Earth surface) are simulated via a low frequency, closedform power series expansion of the electromagnetic fields scattered off an equivalent ellipsoid within a homogeneous, conductive medium, the source itself being idealized as a vertical magnetic dipole nearby. The approach provides formulations amenable to fast yet… 
Spatial dynamics of a timedelayed reaction and diffusion malaria model
15 Jul 2015  8:48 amThis paper is concerned with the spatial dynamics of a timedelayed reaction and diffusion malaria model. We first analyse the wellposedness of the initialboundary value problem of the model. Then, we study the global stability of the diseasefree or endemic steady state for the system by structuring two Lyapunov functionals. Moreover, by applying Schauder fixedpoint theorem, we establish the existence of travelling wave solutions connecting the two steady states: the diseasefree steady state and the endemic steady state if the basic reproduction ratio $\mathcal {R}_0 > 1$, and show the… 
European option pricing with transaction costs and stochastic volatility: an asymptotic analysis
15 Jul 2015  8:48 amIn this paper, the valuation problem of a European call option in the presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the option price is obtained. While the dominant term in the expansion is shown to be the classical Black and Scholes solution, the correction terms appear at O(1/2) and O(). The optimal hedging strategy is then explicitly obtained for Scott's model.

WordPress Tag: Mathematics

An open letter to Dr. Palmer, the killer of Cecil the Lion
31 Jul 2015  9:15 pmDear Dr. Walter J. Palmer: Because of your “adventure” in Zimbabwe, you are now the most famous dentist in the world. You recently have admitted to killing Cecil, a 13yearold lion that is the best known lion in Zimbabwe. Cecil was lured from a wild life sanctuary with bait, shot with an arrow by you, tracked for 40 hours, and finally shot dead with a rifle and then beheaded and skinned. No doubt, this would be another trophy to add to your huge collection (you are known to be an experienced hunter with 43 kills of exotic animals under your belt). However, Cecil was wearing a GPS… 
the reveries of a solitary wa*ker: wa*k 4 (universal matters)
31 Jul 2015  5:28 pmcould someone be spreading BS over the internet? The universe is more turbulent than we imagined. It’s a quantum computer. It’s nothing but information. Where’s all the lithium? Is it really spinning, and are we anywhere near the axis? What was in the beginning? Pure energy? What does that mean? Energy without particles? The energy coalesced into particles, so I’ve read. Sounds a bit miraculous to me. The fundamental particles being quarks and electrons. Leptons? But quarks aren’t leptons, they’re fermions but leptons are also fermions but these are but names. Quarks came together… 
About Completeness
31 Jul 2015  3:23 pmAbout this Quote These words were said by David Hilbert during his lecture “Mathematical Probl 
Arts Review: The Amazing World of MC Escher.
31 Jul 2015  1:23 pmMy lack of patience with M.C. Escher is a thread which I can trace all the way back to a definite be 
Maths, maths, maths!
31 Jul 2015  12:16 pmToday I have wrestled with weighted linear regression, multiplying and inversing matrices and trying to convert an extremely complex excel spreadsheet full of formulae I had never seen before in my life into a PHP function! So that was fun! Still I am not as bad as this guy. http://www.theladbible.com/articles/somepeopleontheinternetarereallystrugglingwithquitesimplemaths

MathNotations

Balanced Learning is not Blended or Flipped
30 Jul 2015  4:53 pmHaven't been up to one my passionate rants in a long time so buckle up...Technology has enabled educators to reimagine the traditional classroom, how students learn and how we facilitate this process, aka teach. Incredible new opportunities to empower students to take more control over their own learning in a "spacetime continuum" sort of way. Not to mention providing powerful tools to analyze data to individualize and maximize learning. Are there any buzzwords I omitted!BUT...We have strayed from NCTM'S central message from over 25 years ago: ***BALANCING*** PROCEDURAL LEARNING and… 
Modeling  What Algebra Looks Like on the New SAT/PSAT and the Common Core
28 Jul 2015  6:20 pmOn twitter.com/dmarain...A bear population, P(t), after t yrs, is modeled by P(t)=Mk(t20)², 0≤t≤20. Initial population:356 Max pop'n:500 Estimated population after 10 yrs? Answer: 464COREFLECTIONSIs this the "new" algebra? Students given a function with PARAMETERS which "models" real world data? Questions like this have appeared on SATs for a few years now and, based on the sample new SAT/PSATs released by the College Board, they will become even more common. Students will be asked to analyze the function and use it in application. The Common Core also emphasizes algebra models … 
37 not 42 the Answer to The Meaning of Life? A Common Core Investigation
25 Jul 2015  3:31 amFrom twitter.com/dmarain...A Middle School Common Core InvestigationIs 37 an "interesting" #?37x4=148; 41="3",81="7" 37x13=481 37x22=81437x5=185; 85="3",81="7" 37x14=518 37x23=851How far can you extend the pattern?And is 37 patriotic (apologies to AK&HI)??37x48=1776And my favorite ...1/37=0.027027... 1/27=0.037037...Is it all because 37x3=111?First we engage, then illuminate...VISIT ME DAILY ON TWITTER AT twitter.com/dmarain 
Parabolas, NEW PSAT/SAT and the Common Core
20 Jul 2015  10:11 amAs posted on twitter.com/dmarain... SHOW: The line with slope 1 intersecting y=(xh)²+k at its vertex also intersects at (h1,k1). COREFLECTIONS How would you modify this to make a gridin or multiple choice question? A question similar to this appears on the published practice NEW PSAT. It is one of the last 34 questions on the gridin with calculator section and was rated "medium" difficulty. I would rate it as more difficult! I recently tweeted the link for this practice test but easy to find on the College Board website. Do the parameters h,k discourage use of graphing… 
Median = Geometric Mean? A Common Core Investigation
18 Jul 2015  4:12 pmAs tweeted on twitter.com/dmarain... J noticed that for an arithmetic sequence like 3,7,11,15,19 the median equals the arithmetic mean. In this case, the median and "mean" are both 11. She found this was wellknown and not too difficult to prove. She wondered if there was an analogous rule for geometric sequences like 2,4,8,16,32. Instead of the arithmetic mean she tried the geometric mean: (2•4•8•16•32)^(1/5) which equals 8, the median. VERIFY THIS WITHOUT A CALCULATOR! Unfortunately her conjecture failed for a geometric sequence with an even number of terms like 2,4,8,16…

Math Bootcamps

Reading scatterplots
9 Jul 2015  1:55 pmScatterplots are used to understand the relationship or association between two variables. Questions like “When the temperature increases, do gas prices also increase?” or “How are changes in the price of gas related to the number of miles people drive each month?” can be answered by studying the pattern in a scatterplot. Basic Structure Given a scatterplot, the variable on the horizontal axis is the predictor (or independent variable) and the variable on the vertical axis is the response (or dependent variable). Using this terminology, a scatterplot is used to… 
Making two way tables
20 Jun 2015  10:35 amTwo way tables, also known as contingency tables, show frequencies (counts) as they relate to two variables. As usual, we will use an example to see how they work! Example Suppose that a company is doing market research on a new product and have selected a random sample of potential customers to help choose the most effective TV commercial. Out of the 180 people in the sample 65 viewed the first version, 30 viewed the second version, and the remainder viewed the third. Of those who viewed the first version, 25 indicated that they were likely to buy the product while the rest said they were… 
Scatterplots on the TI83 or TI84 graphing calculator
19 Jun 2015  4:04 pmScatterplots are used to visualize the relationship or association between two variables. For example, can you say in general that studying more will result in higher grades? We could investigate this by collecting data on how long students studied and perhaps their grade on a final exam and then creating a scatterplot. The overall pattern would help us determine what kind of association time spent studying has with final exam grades. On the TI83 or 84 series of graphing calculators, getting a scatterplot is pretty easy. Let’s use an example data set to walk through the process. Example… 
How to read a boxplot
14 Jun 2015  11:33 amBoxplots are a way of summarizing data through visualizing the five number summary which consists of the minimum value, first quartile, median, third quartile, and maximum value of a data set. If a data set has no outliers, a boxplot will be made up of the following values. But, if there ARE outliers (those are values that fall far from the main pattern of the dataset), then a boxplot will instead be made up of the following values. As you can see above, outliers (if there are any) will be shown by stars or points off the main plot. If there are no outliers, you simply won’t see those… 
Common shapes of distributions
13 Jun 2015  5:18 pmWhen making or reading a histogram, there are certain common patterns that show up often enough to be given special names. Sometimes you will see this pattern called simply the shape of the histogram or as the shape of the distribution (referring to the data set). While the same shape/pattern can be seen in many plots such as a boxplot or stemplot, it is often easiest to see with a histogram. In the examples below, we will look at each of these shapes and some of their important properties. Bell shaped / symmetric Histograms that are bell shaped/symmetric appear to have one clear center that…

Institute for Mathematics and Computer Science

IMACS Expands to New Locations in Delray Beach and Pembroke Pines!
24 Jul 2015  6:30 amWhen it comes to providing their children with the lifelong benefits of genuine learning, South Florida parents know where to go — IMACS! For over 20 years, the Institute for Mathematics and Computer Science has been giving students an outlet for reaching their highest potential in math, computer science and logical reasoning. IMACS teaches its unique classes afterschool at its own centers as well as at many of the top private schools in the tricounty area, including Pine Crest, American Heritage and University School. To meet the growing demand for its classes, IMACS is expanding to… 
IMACS Wishes You aHappy Independence Day!
2 Jul 2015  6:06 amThe IMACS Blog is taking a short summer hiatus and will return next month. Have a safe and happy 4th of July! Looking for an incredibly fun summer experience that exercises the mind? Check out IMACS’ HiTech Summer Camp! Like IMACS on Facebook for the latest information about our local classes and online courses. 
Slowing Down to Get Ahead in Math
3 Jun 2015  10:00 pm"The classrooms that produce high achieving students are those in which students work on deep, rich mathematics through tasks that they can take to any level they want. No one is told what level they can reach and no one is held back by narrow questions that limit studentsâ€™ mathematical development and creativity." —Jo Boaler, Professor of Mathematics Education, Stanford The above quote comes from a recent article by Stanford professor Jo Boaler. Professor Boaler, through her Youcubed organization, advocates for valuing depth and creative problemsolving over… 
Motivation and the Gifted Child
6 May 2015  10:00 pm"My kid could finish his math homework in no time if he would just do it, but instead he drags it out for an hour, and that’s with me having to nudge him through it." Sound familiar? Parents and teachers often assume that a gifted child will automatically be a high achiever given the child’s high abilities, so it comes as a surprise when he or she underachieves. There can be a variety of reasons for underachievement, but a common cause is lack of motivation. Whereas bright students often enjoy working toward external recognition for their accomplishments, gifted learners… 
11YearOld Davidson Young Scholar Scores Perfect 800 on SAT Math Test
8 Apr 2015  10:00 pmIMACS student Shiva Oswal and his parents pose in front of the magnificent Atlantis Hotel on a family trip to Dubai. When fewer than 1% of 2014 collegebound high school seniors attain a perfect 800 on the math section of the SAT, you know that you’ve met someone special when he’s achieved that amazing feat before even cracking the teen years. That someone is Shiva Oswal, a precocious 11yearold from Northern California who recently earned that lofty score as part of a program through Johns Hopkins’ Center for Talented Youth (CTY) called the Julian C.

mathrecreation

regular polygons, in rings
20 Jul 2015  9:01 pmLooking at the Kepler pentagonal tiling, you may notice the nice looking rings of pentagons around the decagons.You can also make up other tilings with these rings of pentagons  to get the one below to work you have to sneak in some dented or overlapping pentagons.But which regular ngons can form rings like this? You obviously can't do it with a square.And some regular ngons, like heptagons, nonagons, decagons, and hendecagons (11gons) don't work either.All the angles of the regular ngon are (n2)pi/n  so the angles of the polygon in the center would have to be 4pi/n, but for that… 
regular polygons, intersecting regularly
3 Jul 2015  11:54 amLooking through the chapter on the number 5 in the really engaging book Single Digits: In Praise of Small Numbers, by Marc Chamberland, I came across an image and description of Kepler's pentagonal tiling, which looks like this:Kepler Pentagonal TilingThis tiling is made of pentagons, pentagrams, decagons, and fused decagons. Both the decagons and the fused decagons can be made from combinations of regular pentagons and dented pentagons (by dented, I mean in the way described here), so this tiling could also be made with pentagons, dented pentagons, and pentagrams.Decagons and fused… 
regular polygons, dented and sliced
12 Jun 2015  8:13 pmA while ago, l noticed that sliced up octagons made nice tiles.In particular, octagons that are split in a particular way into a dented octagon and a rhombus are pretty neat. These rhombuses are formed from so that they share with the octagon two adjacent sides of the octagon. The dented octagon is formed by slicing off the rhombus. Four of those dented octagons can be put around a vertex to form a pinwheel pattern, and four of the rhombs can be added to that pinwheel to make a bigger octagon.You can do this sort of rhombic slicing with any regular polygon with more than 4 sides (you could… 
octo rhomb
30 May 2015  1:28 pmRegular octagons cannot be used to tile by themselves  if you try, you will find there are square gaps that need to be filled.If you slice a rhombus off your octagon, you'll end up with two tiles  a rhombus and a dented octagon.Each of these shapes can be used to tile by themselves, or tile together. The rhombbyitself tiling is easy to visualize (imagine a squashed grid), here is the dentedoctagon tiling:Now, here's something else: you can take four of these rhombically challenged octagons to make a bigger octagon:You get a nice tree shape if you remove two rhombs from the original… 
octagonal iteration with GSP
14 Apr 2015  6:51 pmHere is a little GSP iteration that I came across that I thought was worth sharing.Start with a line segment  this provides the only "free" points in the sketch  everything else is constructed on top of this, starting with a square based on AB.Next, construct the center of the square, and a circle centered on that square's center and diameter equal to the diagonal of the square.Next, construct points on the circle midway between the points provided by the corners of the squares.We'll iterate by mapping the original line segment onto pairs of these points (in GSP you can select the free…

Maths Tips From Maths Insider

Does Your Daughter Lack Math Confidence? She’s Not the Only One.
31 Jul 2015  5:09 amA recent study by the OECD (Organisation for Economic Cooperation and Development) has highlighted the problem of girls’ lack of math confidence. From the report: Girls “lack selfconfidence” in their ability to solve mathematics and science problems and achieve worse results than they otherwise would, despite outperforming boys overall Girls do worse at math and sciences than boys, even though they do better in other subjects. This gender gap occurs in the majority of countries who took part in the PISA (Programme for International Student Assessment) tests, but the gap in the… 
How Can I Help You Help Your Child With Math?
23 Jul 2015  2:13 amIt’s been over 2 years since I blogged here on Maths Insider! So the first thing I’ll say is I’m sorry! I’ve still been connecting with Maths Insider readers through my Maths Insider Facebook page but have neglected those of you who have been coming over here for advice on helping your child with math. So what has Maths Insider been up to for the past 2 years? 1) Working with Tabtor Math For the past 2 years,I’ve been Tabtor’s instructor for International students looking after families everywhere from the UK to Europe to Asia and lots and lots of… 
How to Solve a Physics Problem (FUNNY!) plus Mental Math Tips
4 Apr 2014  8:14 amI saw this cool comic strip below, by the funny folks at Saturday Morning Breakfast Cereal (SMBC), a few weeks ago on Facebook , and spent a good few minutes crylaughing (is that a thing?) Even my daughter in the midst of wrangling with quadratic equations in preparation for a math test, joined in. You see, even for seasoned math teachers, math lovers and professional scientists and mathematicians, arithmetical errors are all too common when problem solving. As part of my role as Instructor for International Students at Tabtor Math, I was given 5 math worksheets at Grade 5 and 6… 
Check out These Challenging Online Math Tools for Gifted Kids
3 Dec 2013  1:28 amThis is a guest post by Joseph Rodriguez While many educators agree that it is essential to improve the quality of math education in our public schools, a debate persists about how it should be done. Do we work with the students who are struggling, so that they can do better? Or do we push the students who are excelling, so they can move on to even greater things? Budgets are tight and many schools are pushed to decide one path or the other. Fortunately, many online resources can challenge gifted math students with new coursework and an outlet for their ingenuity. Here’s what you… 
Holiday Math and More
28 Nov 2013  1:12 amIf you’ve read my Tabtor vs Kumon blog post a few months back, you’ll know that I’ve been working with Tabtor Math, the personalized iPad based math program. I’m Tabtor’s instructor for many of their international students, and I’m also recording instructional videos which accompany each of the Tabtor worksheets as well as writing articles for their blog. As a result, It’s been a bit quiet here at Maths Insider but after the holiday I’ll hopefully be back here with a vengeance. I’ve still got plenty of ideas to share with you on Maths…

MathFour

Talking About Guns at School
29 Jul 2015  12:09 pmI have a concealed handgun license. I own a couple of pistols and enjoy shooting them. I like to shoot trap and skeet. And I’m married to a lifetime member of the NRA. You could say I like guns. Being a teacher and liking guns is a bit of a challenge, though. When students talk about guns, I have to be careful. I don’t want to lie (it’s tough earning trust as a math teacher these days). But I don’t want to encourage inappropriate conversations. I talk about talking about guns. That’s not a typo. I talk about talking about guns with my students. If you try to… 
Zentangle – Meditation, Art, Math!
20 Jul 2015  4:13 amMy cousininlaw recently introduced me to this cool “doodling” method called Zentangle. I’ve been doing it quite a bit – especially since it’s far more socially acceptable to draw than check twitter during meetings. ahem… Zen… WHAT? Zentangle. Zen TANGLE. So it’s Zenish (meditative, calm, relaxing), using tangles (like doodles, but more intricate and structured). Each tangle is a design using circles, line segments, curves and/or shading. You repeat the tangle into a pattern, adding variety in size, shape or orientation to make some really… 
Your Students Are Individuals
17 Jul 2015  1:58 amI was so sad to when I made the decision to resign. For the last year I’ve been teaching students with diagnosed neurological differences. They’ve been remarkable from so many perspectives. But when I told one of the administrators how much I’ll miss them, the response was a cool, “There are always more students.” Interchangeable Students This flippant comment didn’t sit well with me. Of course there are always more students. But saying this implies that this year’s students are merely “numbers.” Numbers that can be interchanged with next year’s students. Just… 
Texas Instruments Little Professor
15 Jul 2015  11:05 amThis morning I featured the Little Professor “electronic calculator” by Texas Instruments on episode 23 of #KnickKnackYack in the #MathShack. It was so cool and so much fun, I wanted to share it here. If you’re old enough, you might remember having one of these. Or coveting it because your friend had it. And if you’re geeky enough, you might remember actually playing it. You can find the vintage Little Professors here or buy a fancy new Solar Little Professor from TI here. And you can share this on Twitter, Facebook and even Pinterest! I do #KnickKnackYack in the… 
Smurfy Student Traits You See in Yourself
3 Jul 2015  9:00 amThis past year I’ve had the incredible joy of teaching a group of students with diagnosed neurological differences. I like to think they learned from what I had to offer them. However, I learned so much more from them. Specifically about myself. Girl, Intensified One of the coolest things about this student population is that their differences make some of their characteristics much more intense. If a student was inclined to frustration, and got frustrated, he would get really really frustrated! Often these intense characteristics were so dramatic that it would drown out other…

Mathforallgrades Blog

Jul 8, Interior Angles
8 Jul 2015  3:03 amAngles formed between the sides of any polygon are called interior angles 
Jun 17, Exponents rules
17 Jun 2015  12:22 amExponents rules enable arithmetic expression of base and index. 
May 26, Distributiveproperty
26 May 2015  3:18 amdistributive property distributes an arithmetic operation over others such as addition, multiplication.. 
May 12, 10thgrademath
12 May 2015  12:11 am10th grade math consisting of algebra, arithmetic, geometry, coordinate geometry, statistics. 
Feb 9, algebra 1 help
8 Feb 2015  10:04 pmalgebra 1 help includes data analysis tools, functions, equations, inequalities, exponents, polynomials, quadratic equations

MIND Research Institute Blog

Off the Number Line: We Struck Gold!
30 Jul 2015  9:00 amInterviewer: Oh, I get it… They are mining for numbers. Cartoonist: Yes, but look at the awesome number they found! That's the golden ratio: 1.61803398875... Interviewer: I've heard of the golden ratio before, but I never knew it was approximately 1.618. Why is it called “golden”? Cartoonist: It’s "golden" because it has so many beautiful mathematical properties. This irrational number is often written as phi (φ) after the Greek artist Phidias who used this aesthetic ratio in his sculptures that were often literally made of gold. Interviewer: Now I know what to make my mathcrazed… 
Let's Turn Learning Inside Out: Learning from Failure
28 Jul 2015  9:00 amThis post was originally published on Huffington Post ImpactX. Janine Ingram is the Vice President of Philanthropic Partnerships at MIND Research Institute. Like most parents this summer, I went to see "Inside Out." Unlike most, I went alone. It was on my oldest son's birthday and I wanted to honor our birthday tradition of going to a family movie, despite the fact my newly minted 21yearold was 860 miles away playing basketball with his Idaho State University teammates. I started crying as I took my seat, realizing our tradition had run its course since both boys are now ginormous men… 
Off the Number Line: Rational Vs. Irrational Numbers Cartoon
23 Jul 2015  10:18 amInterviewer: What are we looking at here? Cartoonist: At the top we have a group of famous irrational numbers, φ, π, e and √2. Hiding behind a wall at the bottom we have two fractions. The 1/5 fraction is saying to the 3/4 fraction: "Ohno... we're outnumbered!" Interviewer: And... why is this funny? Cartoonist: At the surface level, we have numbers saying they are "outnumbered." This is already funny. Hahahaha... Okay, now that we've composed ourselves, let's explore the depth of the joke here. Back in the time of Pythagoras, people refused to believe that these crazy irrational… 
The Role of Parents and Teachers in Gamebased Learning
21 Jul 2015  9:00 amInterview with Greg Toppo and Matthew Peterson Part 3 In our final installment of the series, reporter and author Greg Toppo continues the discussion with ST Math creator Matthew Peterson about gamebased learning. In his new book, The Game Believes in You, Toppo interviews Peterson and other leaders in the educational game field for an indepth look at the potential of gamebased learning to be, yes, a gamechanger in education. Peterson and Toppo recently discussed some of their biggest personal revelations about games, and what they see as the role of teachers and parents in educational… 
DIRECTV Celebrates Fun, Learning and ST Math in Denver
14 Jul 2015  9:00 amDIRECTV and FOX visited Denver’s University Prep Elementary School (U Prep) during the last week of their 20142015 school year to host a liveaction version of the hit TV show “Are You Smarter Than a 5th Grader.” Stephen Demedis, a member of DIRECTV's Coporate Communications team based at DIRECTV's Denver, Colo. Office, was in attendance and wrote the below blog, which was orginally posted on the DIRECTV GOES TO SCHOOL website. I am smarter than a fifth grader. And I’ve been certain of this since the mid90s. But as I stood in the back of the gymnasium at…

Teach Math for Free

5 Interesting Facts & PowerPoint Presentation about Pythagoras theorem
29 Jul 2015  10:52 amI have put together some very interesting facts about Pythagoras for kids. In order to help our readers who are teachers, I have also prepared a powerpoint presentation on the theorem. My last post dealt with the trapezoid as a part of the geometry curriculum. Pythagoras of Samos, as he is known, was a Greek mathematician and an ancient philosopher. When did Pythagoras live?Although there is limited verified literature available on the life of Pythagoras, he is believed to have lived between 580BC – 500BC hailing from the Greek Island of Samos. An article on the BBC webportal… 
What is the formula of the Area of a Trapezoid: Geometry Curriculum
26 Jul 2015  2:29 amHi there, Today, as a part of the geometry curriculum, I am going to address one critical question that readers have been frequently asking – “what is the formula of the area of a trapezoid”. In my previous posts I had written about circles and Triangles. Well, before I dwell directly into Area, I will define a few basics: Trapezium or Trapezoid : Are they the same?Yes, Trapezium and Trapezoid refers to the same geometric figure. The former is defined in the UK while the latter is so called in the United States. Define trapezoidA trapezoid is a four sided geometric figure having one… 
Print Flashcards Online  Interactive Math Activities
21 Jul 2015  4:17 amPrint Flash Cards OnlineAfter my post on Effective common core strategies for math teachers, I have been constantly receiving requests to suggest if there are resources/ websites that could be used to print flash cards online. Today, I wish to address this query with this post. The importance of making a class interactive is a concept every mathematics teacher strives for. There are various visual learning strategies that are available that could be adopted to achieve this purpose. One such method is the flash cards. When concepts such as addition, subtraction,… 
Effective common core strategies for math teachers  Instructional Strategies for teachers
12 Jul 2015  10:19 pmI have often wondered how teachers deliver a good lecture. What might be the secret behind conducting a good, informative, effective math class. Preparing for a math class is a critical process that a math tutor goes through every day before her class. Today’s post tries to highlight some of those preparative steps:1. An effective Math class requires a teacher to prepare a definite lesson plan – Reaching out to students effectively is the topmost priority for a math tutor; this requires the tutor to prepare a sound lesson plan. A lesson planner acts as a blue print/ road map… 
Learn Problem Verification  Help for Math Problems Verification
26 Jun 2015  2:09 amHey there, I have always been looking for methods to cross verify problems (be it addition, subtraction, multiplication or division) while writing any competitive exam. I have also had my juniors approach me for some help with math problem verification. During exams, we are short of time and always want to ensure that answers are right. The importance of result verification is often under emphasized. You might be an ace mathematic question solver but verification is a critical process in itself.The concept of Vedic Mathematics has defined a few rules to assist in cross…