In the developed world, there's a pretty consistent relationship between the economy and childbearing: The two rise and fall together. Almost a decade later, though, with unemployment heading toward 4 percent , we're still waiting for births to come back up.


Most Popular Stories

Where Are the Recovery Babies?by Robert VerBruggen It was no surprise ...
Search for "math OR mathematics"20 Nov 2017  2:18 am 
Math at the Met
Scientific American  Math16 Nov 2017  11:45 amAmid the museum’s 2 million works of art lie numerous mathematical curiosities  Read more on ScientificAmerican.com 
The Bridge Wobbles. So Do You. That’s When the Trouble Starts.
Mathematics10 Nov 2017  2:47 pmMathematicians found that bridges wobble suddenly when a critical crowd threshold is exceeded, and developed a model to predict it in future bridges. 
Color Your World: More with Maps, Graphs, and Polygons
Loren on the Art of MATLAB27 Oct 2017  4:22 amToday, guest blogger Matt Tearle continues his investigation of the new polyshape type (added in R2017b) as a mapping tool.ContentsWhere were we?Start simple: a greedy coloring algorithmGreed is good?Adding a little intelligence (but with no guarantees)How far can this go?Where were we?In a previous post, I used the new polyshape variable type in MATLAB to determine connections between states. You can see the code in that post. I'll just load in the polygons and matrix of connections that came from that:load stateborders % Make a graph of state connections G = graph(border,stnames,'lower'); %… 
Math Mammoth Thanksgiving sale
Homeschool Math Blog16 Nov 2017  4:59 amMath Mammoth THANKSGIVING sale is here!Get 25% off of all the downloads/CDs sold at MathMammoth.com site! Use the coupon code THANKS2017.The offer is valid till December 3, 2017.Start browsing!




Search for "math OR mathematics"

Where Are the Recovery Babies?by Robert VerBruggen It was no surprise ...
20 Nov 2017  2:18 amIn the developed world, there's a pretty consistent relationship between the economy and childbearing: The two rise and fall together. Almost a decade later, though, with unemployment heading toward 4 percent , we're still waiting for births to come back up. 
Va. to certify election results, trigger recount requests new
20 Nov 2017  2:12 amVirginia's State Board of Elections is due to certify the results Monday morning of the Nov. 7 races that provided sweeping victories for Democrats up and down the ballot. The certification Monday will allow at least three Democratic candidates in tight house of delegates races to file for recounts . 
Students and Teachers: Tips for Beating the MidYear Slump
20 Nov 2017  2:10 amWhether you're a teacher or a student, staying motivated for the rest of the school year can be a challenge. But, what happens in the classroom counts long after the school year is new. 
Government to focus on technology, maths, engineering at basic level
20 Nov 2017  2:07 amPresident Nana Addo Dankwa AkufoAddo has directed the ministry of education to draw up programmes to strengthen and upscale the study of Science, Technology, Engineering and Mathematics from the basic level. He explained that this was part of educational reforms being undertaken by his government to promote science, technology and innovation in the country. 
What should schools teach?
20 Nov 2017  1:42 amHow refreshing then, that unlike many educational policy prescriptions, What Should Schools Teach? does not offer a dazzling list of innovative academic hybrids, along with an interactively inspirational flowchart of how to deliver them. Rather, the answer is laid out in beautiful clarity, in chapters on mathematics, foreign languages, physics, biology, history, geography, English literature and art  not as an exhaustive list, but the beginning of a conversation about why these core subjects continue to be essential and relevant to the 21stcentury curriculum.



Scientific American  Math

Math at the Met
16 Nov 2017  11:45 amAmid the museum’s 2 million works of art lie numerous mathematical curiosities  Read more on ScientificAmerican.com 
15 Mathematical Curiosities to Celebrate Marie Curie's 150th Birthday
6 Nov 2017  8:00 amSome numerical oddities fall out of this anniversary of the only person to win Nobel prizes in two separate scientific fields  Read more on ScientificAmerican.com 
A Few of My Favorite Spaces: The Loch Ness Monster
5 Nov 2017  7:00 am“They did the math, they did the monster math…”  Read more on ScientificAmerican.com 
The Unforgiving Math That Stops Epidemics
1 Nov 2017  5:00 amNot getting a flu shot could endanger more than just one’s own health, herd immunity calculations show  Read more on ScientificAmerican.com 
Household Chores for Mathematicians
24 Oct 2017  4:00 amNeed a babysitter? Ask a combinatorialist. Baseboards dirty? A number theorist won't mind cleaning them. And other highly scientific recommendations for mathematicians to handle the housework  Read more on ScientificAmerican.com



Mathematics

The Bridge Wobbles. So Do You. That’s When the Trouble Starts.
10 Nov 2017  2:47 pmMathematicians found that bridges wobble suddenly when a critical crowd threshold is exceeded, and developed a model to predict it in future bridges. 
Who Invented ‘Zero’?
7 Oct 2017  12:30 pmThe void is as old as time, but it was a human innovation to harness it with a symbol. 
Vladimir Voevodsky, Revolutionary Mathematician, Dies at 51
6 Oct 2017  10:02 amA oncerestless student who flunked out of college went on to found entirely new fields of mathematics. “He has given us a new constitution,” a colleague said. 
Hints of Trigonometry on a 3,700YearOld Babylonian Tablet
29 Aug 2017  11:44 amScholars have debated for decades the purpose of 60 numbers written on a small clay tablet. Two Australian mathematicians believe they have figured it out. 
Cathleen Morawetz, Mathematician With RealWorld Impact, Dies at 94
11 Aug 2017  11:50 amIn one case, Dr. Morawetz’s work helped aerospace engineers minimize shock waves around the wings of airplanes flying below the speed of sound.



Loren on the Art of MATLAB

Color Your World: More with Maps, Graphs, and Polygons
27 Oct 2017  4:22 amToday, guest blogger Matt Tearle continues his investigation of the new polyshape type (added in R2017b) as a mapping tool.Contents<ul><li>Where were we?</li><li>Start simple: a greedy coloring algorithm</li><li>Greed is good?</li><li>Adding a little intelligence (but with no guarantees)</li><li>How far can this go?</li></ul>Where were we?In a previous post, I used the new polyshape variable type in MATLAB to determine connections between states. You can see the code in that post. I'll just load in the polygons and matrix of connections that came from that:load stateborders % Make a graph of state connections G = graph(border,stnames,'lower'); % Obtain centroid locations for states [x,y] = centroid(p); % Plot map and connections plot(p) hold... 
Loren’s Excellent Adventure: Maps, Graphs, and Polygons
12 Oct 2017  4:21 amR2017b was released recently. Today's guest blogger, Matt Tearle, discovered a fun application of one of the many new features  solving a mapbased puzzle.Contents<ul><li>A traveling MathWorker problem</li><li>Enter MATLAB</li><li>Problem: who is my neighbor?</li><li>Solution: the fat of the land</li><li>Visualizing the results</li><li>Where to next?</li></ul>A traveling MathWorker problem"Car Talk" recently featured a brain teaser submitted by a former MathWorker. The short, slightly modified version is: Loren has to drive from Delaware to every state in the contiguous US, visiting each state exactly once; Loren's boss  let's call him Jack  offers to meet her in the last state, which turns out to be his birthplace; but how can Jack know what the last state will be,... 
Math with Words – Word Embeddings with MATLAB and Text Analytics Toolbox
21 Sep 2017  6:32 amText data has become an important part of data analytics, thanks to advances in natural language processing that transform unstructured text into meaningful data. The new Text Analytics Toolbox provides tools to process and analyze text data in MATLAB.Today's guest blogger, Toshi Takeuchi introduces some cool features available in the new toolbox, starting with word embeddings. Check out how he uses sentiment analysis to find good AirBnB locations to stay in Boston! Contents<ul><li>What is a Word Embedding?</li><li>Ingredients</li><li>Loading a PreTrained Word Embedding from GloVe</li><li>Vector Math Example</li><li>Visualizing the Word Embedding</li><li>Using Word Embeddings for Sentiment Analysis</li><li>Word Embeddings Meet Machine Learning</li><li>Prepare Data for...</li></ul> 
MATLAB and the 2017 Eclipse – Part 4: Imaging the Eclipse
29 Aug 2017  3:57 amToday our guest blogger, David Garrison, will continue his series on MathWorks involvement in the 2017 solar eclipse.<ul><li>Part 1: The Citizen CATE Experiment</li><li>Part 2: Training the Volunteers</li><li>Part 3: Rehearsing for the Eclipse</li><li>Part 4: Imaging the Eclipse</li></ul>Here is Part 4 of the Series.Contents<ul><li>Recap of Parts 1  3</li><li>Getting Ready for the Eclipse</li><li>The Partial Phase</li><li>Totality</li><li>Any Questions?</li></ul>Recap of Parts 1  3In Part 1 of this series, I discussed MathWorks participation in the Citizen CATE Experiment  a citizen science project to image the 2017 solar eclipse. In Part 2 of this series, I described the volunteers, the equipment they will be using, and how they are being trained. In Part 3 of this series, I talked about how the... 
Ways to Perform Calculations on Groups of Data in Tables
9 Aug 2017  6:38 amToday I'd like to introduce a guest blogger, Stephen Doe, who works for the MATLAB Documentation team here at MathWorks. Stephen will discuss different methods for grouping data, and performing calculations on those groups, using Tables.Contents<ul><li>Create Table</li><li>Perform Calculation on Each Numeric Variable</li><li>Perform Calculation on Groups in Numeric Variables</li><li>Multiple Variables as Input Arguments to Function</li><li>Use Groups in Multiple Calculations and Tabulate Results</li><li>Perform Calculations on Tall Table</li><li>Turning the Tables on You</li></ul>Create TableTables are convenient containers for columnoriented data. The variables in a table can have different data types, but must have the same number of rows. You can access table data by row,...



Homeschool Math Blog

Math Mammoth Thanksgiving sale
16 Nov 2017  4:59 amMath Mammoth THANKSGIVING sale is here!Get 25% off of all the downloads/CDs sold at MathMammoth.com site! Use the coupon code THANKS2017.The offer is valid till December 3, 2017.Start browsing! 
Four principles of deeply effective math teaching
9 Oct 2017  5:42 amI went through and thoroughly updated this article of mine... have you read it in the past?Four basic principles of deeply effective math teachingIf you were asked what were the most important principles in mathematics teaching, what would you say? I wasn't really asked, but I started thinking, and came up with these basic habits or principles that can keep your math teaching on the right track.Principle 1: Let It Make SensePrinciple 2: Remember the GoalsPrinciple 3: Know Your ToolsPrinciple 4: Living and Loving Math 
Play With Your Math puzzles
2 Oct 2017  9:13 amAn intriguing website.... problems, but not solutions (not that I can see... but maybe, if you subscribe to get email updates, you'd get the solutions?)https://playwithyourmath.com/Their idea is,We take problems that we love, and we adapt them so that everyone (and anyone) can play. We design posters and handouts that hook you visually and explain the problem in just enough words. The problems that we’ve picked require trying, struggling, failing, adjusting, and trying again until, finally, a discovery is made.I definitely agree... that's what TRUE problem solving is all about! Doing it with math can prepare students for REAL LIFE, where often, the problems they will be facing at the workplace will NOT... 
Tower of Babel and spiritual languages
27 Sep 2017  1:48 pmI invite you to enjoy this Bible study about the tower of Babel, the division of languages there — AND the picture it gives us of SPIRITUAL languages today. 
Math Mammoth printed books sale!
12 Sep 2017  2:03 pmFrom September 12 till September 18, 2017, get Math Mammoth printed books at 20% off atRainbow Resource Center. :)



Denise Gaskins' Let's Play Math

How You Can Play with Math #113 at Three J’s Learning
27 Oct 2017  12:31 pmCheck out the new carnival of playful math for all ages! <ul> <li>Math Teachers at Play Blog Carnival #113</li> </ul> Each carnival brings you a great new collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun. This month we have wholebody math, noticeandwonder puzzles, a game to build math vocabulary, intransitive dice, making sense of trig identities, and playing Go on a hundred chart. And plenty more! Click Here to Read the Carnival Blog Hey, Blogger, Can You Spare a Time? We need help! Do you write an education or family blog? Classroom teacher, math coach, homeschooler, parent, college professor, unschooler — anyone interested in helping kids play around with math? Please... 
Education Bloggers: Share Your Post!
16 Oct 2017  5:06 am[Image by Omar Omar (CC BY 2.0) 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 Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers. Don’t procrastinate: The deadline for entries is this Friday, October 20. The carnival will be posted next week at... 
How You Can Play with Math #112 at Find the Factors
2 Oct 2017  8:03 amCheck out the new playful math blog carnival at Find the Factors blog. Iva put together a great collection of math games, activities, and teaching tips: <ul> <li>896÷8=112. Math Teachers, It’s Carnival Time!</li> </ul> The carnival features comics, literature, talking with kids, favorite numbers, classroom management, a bulletin board that actually gets read, and plenty of math art. Along with several fantastic math puzzles to explore. Click here to go read the carnival blog And if you’re a blogger, be sure to submit your blog post for next month’s carnival! Past carnivals are still full of mathy treasure. Check them out: <ul> <li>Browse all the past editions of the Math Teachers at Play blog carnival</li> </ul> Want to help your kids... 
How to Succeed in Math: AnswerGetting vs. ProblemSolving
21 Sep 2017  4:53 amYou want your child to succeed in math because it opens so many doors in the future. But kids have a shortterm perspective. They don’t really care about the future. They care about getting through tonight’s homework and moving on to something more interesting. So how can you help your child learn math? When kids face a difficult math problem, their attitude can make all the difference. Not so much their “I hate homework!” attitude, but their mathematical worldview. Does your child see math as answergetting? Or as problemsolving? Answergetting asks “What is the answer?”, decides whether it is right, and then goes on to the next question. Problemsolving asks “Why do you say that?” and listens... 
Do You Blog About Math?
17 Sep 2017  11:20 pmby Mike Licht, NotionsCapital.com It’s carnival time again. Activities, games, lessons, handson fun — if you’ve written a blog post about math, we’d love to have you join our Math Teachers at Play (MTaP) math education blog carnival. Posts must be relevant to students or teachers of schoollevel mathematics (that is, anything from preschool up through firstyear calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival. Click here to submit your blog post Don’t procrastinate: The deadline for entries is this Friday, September 22. The carnival will be posted next week at Find the Factors blog. Would You Like to Host the Carnival? Hosting the blog carnival...



Basic mathematics blog

Prove that the Diagonals of an Isosceles Trapezoid are Congruent
19 Nov 2017  12:54 pmProve that the diagonals of an isosceles trapezoid are congruent 
Prove that the Diagonals of a Rectangle are Congruent
19 Nov 2017  7:04 amProve that the diagonals of a rectangle are congruent 
Define and Identify Polygons Worksheet
17 Nov 2017  9:09 amDefine and identify polygons worksheet  great worksheet for students 
Choosing a Factoring Strategy
16 Nov 2017  9:26 amHow to choose a factoring strategy when factoring polynomials? 
Prove that Opposite Sides of a Parallelogram are Congruent
15 Nov 2017  8:44 amProof of the theorem: Opposite sides of a parallelogram are congruent



Computational Complexity

A Tale of Three Rankings
16 Nov 2017  5:42 amIn the Spring of 2018 the US News and World Report should release their latest rankings of US graduate science programs including computer science. These are the most cited of the deluge of computer science rankings we see out there. The US News rankings have a long history and since they are reputation based they roughly correspond to how we see CS departments though some argue that reputation changes slowly with the quality of a department. US News and World Report also has a new global ranking of CS departments. The US doesn't fare that well on the list and the ranking of the US programs on the global list are wildly inconsistent with the US list. What's going on? 75% of the global ranking is based on... 
Can you measure which pangrams are natural
13 Nov 2017  6:48 amA Pangram is a sentence that contains every letter of the alphabet The classic is: The quick brown fox jumps over the lazy dog. (NOTE I had `jumped' but a reader pointed out that there was no s, and that `jumps' is the correct word) which is only 31 letters. I could give a pointer to lists of such, but you can do that yourself. My concern is: a) are there any pangrams that have actually been uttered NOT in the context of `here is a pangram' b) are there any that really could. That is which pangrams are natural? I know this is an ill defined question. Here are some candidates for natural pangrams 1) Pack my box with five dozen liquor jugs 2) Amazingly few... 
Advice for the Advisor
9 Nov 2017  11:08 amA soontobe professor asked me recently if I could share some ideas on on how to advise students. I started to write some notes only to realize that I had already posted on the topic in 2006. Have students work on problems that interest them not just you. I like to hand them a proceedings of a recent conference and have them skim abstracts to find papers they enjoy. However if they stray too far from your research interests, you will have a hard time pushing them in the right directions. And don't work on their problems unless they want you to.Keep your students motivated. Meet with them on a regular basis. Encourage students to discuss their problems and other research questions with other students and... 
The two fears about technology one correct, one incorrect
6 Nov 2017  8:44 amWhen the luddites smashed loom machines their supporters (including Lord Byron, Ada Lovelaces father) made two arguments in favor of the luddites (I am sure I am simplifying what they said): <ol> <li>These machines are tossing people out of work NOW and this is BAD for THOSE people. In this assertion they were clearly correct. (`lets just retrain them' only goes so far).</li> <li>This is bad for mankind! Machines displacing people will lead to the collapse of civilization! Mankind will be far worse off because of technology. In this assertion I think they were incorrect. That is, I think civilization is better off now because of technology. (If you disagree leave an intelligent polite comment. Realize that just be leaving...</li></ol> 
Matching and Complexity
2 Nov 2017  7:44 amGiven a group of people, can you pair them up so that each pair are Facebook friends with each other? This is the famous perfect matching problem. The complexity of matching has a rich history which got a little richer in the past few months. For bipartite graphs (consider only friendships between men and women), we have had fast matching algorithms since the 1950's via augmenting paths. In the 1965 classic paper, Path, Trees and Flowers, Jack Edmonds gives a polynomialtime algorithm for matching on general graphs. This paper also laid out an argument for polynomialtime as efficient computation that would lead to the complexity class P (of P v NP fame). After Razborov showed that the clique problem...



The Math Less Traveled

Fermat’s Little Theorem: proof by modular arithmetic
13 Nov 2017  3:16 pmIn a previous post I explained four (mostly) equivalent statements of Fermat’s Little Theorem (which I will abbreviate “FlT”—not “FLT” since that usually refers to Fermat’s Last Theorem, whose proof I am definitely not qualified to write about!). Today I want to present the first proof of FlT. We’re going to prove statement (2), that is, If is a prime and is any integer not divisible by , then . We already saw that statements (1), (2), and (3) are logically equivalent, so proving (2) is sufficient to prove all of them. (As I’ll show in a future post, we can also generalize this proof to prove the corrected version of statement (4).) So, suppose is a prime, and is any integer not... 
Four formats for Fermat: correction!
1 Nov 2017  9:32 amIn my previous post I explained three variants on Fermat’s Little Theorem, as well as a fourth, slightly more general variant, which it turns out is often called Euler’s Totient Theorem. Here’s what I said: If and is any integer, then . However, this is wrong! We can easily find a counterexample. For example, let and . Then , since there are only two numbers less than that are relatively prime to it (namely, and ; each of , , and shares a common factor with ). But then which has a remainder of , not , when divided by . What’s wrong? It turns out I missed a small but important restriction: this is only true when is relatively prime to . Note this is stronger than saying isn’t divisible... 
Four formats for Fermat
14 Oct 2017  11:35 amIn my previous post I mentioned Fermat’s Little Theorem, a beautiful, fundamental result in number theory that underlies lots of things like publickey cryptography and primality testing. (It’s called “little” to distinguish it from his (in)famous Last Theorem.) There are several different forms in which it is commonly presented, so I wanted to start by introducing them and showing how they are related. Statement 1 Let’s start with the statement that looks the least general: If is prime and is an integer where , then . (Recall that means that and have the same remainder when you divide them by .) For example, is prime, and we can check that for each , if you raise to the th power, you get... 
New baby, and primality testing
30 Sep 2017  1:12 pmI have neglected writing on this blog for a while, and here is why: Yes, there is a new small human in my house! So I won’t be writing here regularly for the near future, but do hope to still write occasionally as the mood and opportunity strikes. Recently I realized that I really didn’t know much of anything about fast primality testing algorithms. Of course, I have written about the LucasLehmer test, but that is a specialpurpose algorithm for testing primality of numbers with a very special form. So I have learned about a few generalpurpose primality tests, including the RabinMiller test and the BaillePSW test. It turns out they are really fascinating, and not as hard to understand as I was... 
From primitive roots to Euclid’s orchard
26 Jul 2017  9:34 amCommenter Snowball pointed out the similarity between Euclid’s Orchard… …and this picture of primitive roots I made a year ago: At first I didn’t see the connection, but Snowball was absolutely right. Once I understood it, I made this little animation to illustrate the connection more clearly: (Some of the colors flicker a bit; I’m not sure why.)



eon

Google Books Ngram
1 Nov 2017  5:57 pmPak’s history of the Catalan numbers mentioned an Ngram chart. But perhaps because I wasn’t reading carefully or possibly due to the fact that I was reading the print copy and did not access url pointing to the said chart, I did not find out about this tool until today. Here’s the link 
Faraday
26 Aug 2017  6:30 pmCompared to mathematics, physics is extremely wellfunded. For example, I have attended many talks by Nobel Laureates compared to Fields Medalists. (Locally, I have attended talks by Serre, S.T. Yau and Pierre Louis Lions. I somehow missed talks by Smale and Ngo Bao Chao. Overseas, I have heard Bhargava and Tao lecture.) But back to physics, in addition to the Nobel Lauretes, there have been many public talks on quantum mechanics, cosmology and particle physics, in relation to the LHC. The latest was on 25th August by David Gross. He mentioned that Faraday, as an answer to the question what was his discovery good for, was said to have answered “you will be able to tax it.” A quick search on the web would... 
What are the chances that a bird will poop on my car?
17 May 2017  6:30 pmThis question was posed as a scenario of mathematics in everyday life. Some googling led to Randall “XKCD” Munroe’s post here. Borrowing similar ideas leads to my own computation below. I park at an open air carpark for work. The easy assumptions are my car has a 4.3m x 1.75m footprint and I park for 8 hours a day. For data on birds, after some searching I found a 2016 article that estimates (provided I interpreted correctly) a total of 377 birds in 113 hectares of builtup area at another university in the country. So if we assume a similar bird population here and that birds poop uniformly everywhere once every hour, [tex] \frac{377}{113 \times 10,000} \times 8 \times 4.3 \times 1.75 \approx 2\% [/tex]... 
Queen of Mathematics
9 Apr 2017  5:26 pmNumber theory has been called the Queen of Mathematics. Until some fifty years ago, it did not occur to anyone that number theory, especially the study of prime numbers, would have any immediate applications to business. More recently, the Queen has been relegated to be the object of a courtship, inspired by material gains, rather than awe. As a result, progress has been made in unexpected directions, which have required deeper investigations. — Papa Paulo A.K.A. Paulo Ribenboim from his pseudonovelnumber theory text “Prime Numbers, Friedns Who Give Problems: A Trialogue with Papa Paulo” (p. 50). 
Triangular numbers modulo powers of 2 and its generalizations
14 Mar 2017  5:54 pmSomeone discussed with me an interesting problem that he was working on with his students. They found that the congruence [tex] \frac{1}{2}X(X+1) \equiv a \pmod{n} [/tex] has a solution for every [tex] 0 \le a n [/tex] if and only if [tex] n =2^k[/tex]. My first instinct of course was to complete the squares for triangular numbers and reduce the problem to [tex] X^2 \equiv a \pmod{n} [/tex]. This turn out to work well for odd modulus and the solutions for triangular numbers and squares correspond. But when the modulus was a power of 2, completing the square would not work. A simple search found a few websites where the phenomenon was recorded and it seems a (perhaps original?) source is Knuth’s the Art of...



WordPress Tag: Mathematics

Measure Theory
20 Nov 2017  2:38 amI had decided to write here a summary of what I read about measure theory but I found a very nice (wellorganized and concise) paper on the topic. So I just repost it here. Enjoy! Measure Theory, John K. Hunter 
HOMEWORK AS ON 20.11.17
20 Nov 2017  1:16 amDear Learners Homework for today…20.11.17 
Cheaper by the Dozen by Frank B. Gilbreth and Ernestine Gilbreth Carey (1948)
20 Nov 2017  1:03 amThe book Cheaper by the Dozen (which is nothing like the 2003 Steve Martin film of the same name, thank goodness) tells the hilarious — and inspiring — true story of the Frank and Lillian Gilbreth family. Frank Gilbreth was a loud and colorful, selftaught engineer who became a worldrenown timemotion expert in the early 1900’s. Lillian, his wife, was a quiet and refined woman who earned a Ph.D. in psychology from Brown University and is considered the firstever industrial/organizational psychologist. Together they changed manufacturing efficiency around the globe — but this memoir (written by two of their children) tells how they also used their groundbreaking timemotion discoveries to run their... 
MATHS BITE: Wythoff's Game
20 Nov 2017  1:00 amWythoff’s game is a twoplayer mathematical strategy game. It is played with two piles of counters and goes as follows: Players take turns to remove counters from one, or both piles (if they are removing stones from both piles, they must remove the same number of stones from each). The game ends when one person removes the last counter, or counters, thus winning. It is name Wythoff’s game, as it was Dutch mathematician W. A. Wythoff that published a mathematical analysis of the game in 1907, although it was previously know in China as tsyanshidzi (“choosing stones”). Optimal Strategy? Any position of the game can be described by a pair of integers (x,y) where x≤y. This describes the size of both piles... 
Eraserhead (Games on Circles I)
20 Nov 2017  12:55 amThis is not about the film by David Lynch. Eraserhead is played by two players on finite graph with some vertices occupied by erasers. At each turn, the player chooses one eraser, moves it to an unoccupied adjacent edge, thereby erasing the connecting edge. The player who moves last wins. Let’s analyze this for cycle graphs. If played with just one eraser, the first player chooses the direction, and all other moves are forced, until the eraser has erased all edges. So the first player wins if the cycle graph has an odd number of vertices. That was boring. For two erasers, it gets slightly more interesting, but the outcome is the same: The first player can win if the number of vertices is odd. The two...



Neoformix

Toronto Coffee Shop Territories
18 Nov 2017  3:30 amA week or so ago I put together a simple project illustrating the locations of coffee shops within the Toronto area. I was curious about the density of coffee shops within the city and also the distributions of the larger coffee chains. In the image below the small dots are locations and the areas are coloured based on the closest location. The colours are Red  Tim Hortons, Green  Starbucks, Yellow  Second Cup, Purple  Coffee Time, Orange  Country Style, Blue  Other. The Tim Horton's red dominates much of the geography outside of the city and the location density is obviously much higher in the downtown area. Zooming in to downtown shows a more fractured landscape with strong... 
Ten Years
8 Apr 2016  4:30 amToday is the tenth anniversary of my first post on Neoformix! Thank you all for your attention and feedback over the years. I never dreamed I would be doing this for so long but it's been great fun. Thank you also to all the creators of interesting and informative work in the field of data visualization and creative coding. I have written 368 posts over the ten year span and they are all available in the Archive. The pace of new posts has slowed down lately but I'm very active on Twitter and Pinterest. 
Pinterest Boards
17 Dec 2015  2:30 amI have been using Pinterest for the last few years to collect images related to my areas of interest. There are over 1000 images pinned so far and you may find them interesting. Take a look! 
Stars and Stones
5 Nov 2014  3:00 amI just launched my first mobile app. It's a game, called Stars and Stones, and you can download it now on the Apple App Store for free. I enjoy games that have a simple natural user interaction, are easy to learn, but have a rich depth of play  an elegant complexity. That's what I attempted to create and I think I came close in many respects. Stars and Stones is a series of dynamic puzzles that get progressively more challenging. There are over 100 levels and the first 50 are free. In each puzzle you drag a token around to try and capture five stars while avoiding stones. The stones move as you move and their speed is relative to your own  the faster you move, the faster they... 
A Short Reflection on Storytelling in Data Visualization
28 Apr 2014  6:15 amThe role of storytelling in Data Visualization has become much discussed over the last year or so. One reason I find this aspect of Data Visualization so interesting is that my own natural tendencies are to focus on exploratory visualization. Much of my own past data visualization work is weak in the storytelling side of things. Coming from a scientific background and personally enjoying the act of discovering patterns in data means my default approach is to build exploratory tools. For me, personally, this whole storytelling aspect seems a rich area to mine in order to improve my work. I just finished listening to the latest Data Stories podcast called Visual Storytelling which is a discussion...



mathrecreation

the island of knights and knaves
18 Nov 2017  6:16 amThere is classic type of logic problem where we are asked to imagine an island consisting of two types of people: those that always tell the truth (knights), and those that always tell lies (knaves). In puzzles based on this trope, the islanders make statements, and we have to figure out which islanders are knights and which islanders are knaves.This pagewill generate knight and knave puzzles of varying difficulty. Here’s an example: An "easy" puzzle from https://dmackinnon1.github.io/knaves/ The grandfather of all these puzzles is an actual islander who referenced an actual island  around 600 BCE, the Cretan Epimenides is credited with the statement “All Cretans are liars.” The fun has not... 
trihexagonal & rhombille tilings
10 Nov 2017  12:14 pmThe image above is the superposition of two tessellations. The dark bold lines show a tiling of the plane that is made up of regular hexagons and triangles (thetrihexagonal tiling).The light lines show portions of the reciprocal (or dual) of the darklined tessellation.To create a reciprocal tessellation, for every two adjacent tiles in the original tessellation, join the centers of the two tiles by a line segment perpendicular to their shared side. This line segment becomes the edge of one of the tiles in the reciprocal tessellation.The reciprocal of trihexagonal tiling is made up entirely of rhombs, the rhombille tiling. 
Diophantine Desmos
23 Oct 2017  11:58 amIt may happen that you have a real valued function, but only want to find those points where both the input and output are integers.For example, consider y = sqrt(x). Suppose you had a graph of sqrt(x) and wanted to show which values of x give an integer result for y, i.e. which values of x are perfect squares:y = sqrt(x) with only integer solutions shownI recently learned how you can find and display integer solutions for certain types of equations in Desmos, and thought I would write a post about how to do this.When we care only about the integer solutions of an equation, we refer to it as a Diophantine equation. In general, Diophantine equations can take many forms  the technique described here can be... 
a Truchet puzzle mystery
3 Oct 2017  6:53 pmI thought it would be fun to create a page of Truchet puzzles, and while doing this I noticed something that surprised me: even though they were randomly generated, all puzzles of the same size had the exact same level of complexity.a single puzzle piecethat can be rotated into 4 positionsIn these puzzles, Truchet tiles like the one above are used to create a specific pattern. All the pieces are the same  it is just a question of rotating them correctly to make the pattern you are aiming for.a Truchet puzzle: can you make this patternusing only Truchet tiles?We can make these Truchet puzzles a bit more interesting if we have a specific starting arrangement, and add the restriction of using the smallest... 
a polynomial division calculator
15 Sep 2017  11:28 amMany visitors to this blog come to see the posts about dividing polynomials using the grid method (like this one). A while ago, I put up a page which generates examples that (hopefully) illustrate this method.Well, I am excited to say that the examples page has been enhanced with the addition of a simple calculator, which allows you to provide your own polynomials for dividing.This is not a sophisticated calculator  the polynomials you provide need to be in expanded form, and they have to be single variable polynomials using "x" for the variable  don't try to be fancy or tricky, please.For example, you may want to try something like this:After you provide your polynomials, hitting the calculate button...



Motion Math

A new home for Motion Math
8 Nov 2017  6:46 amSince founding Motion Math in 2010, our mission has been to help children find delight in intellectual challenge. Today we’re excited to announce that we’ve been acquired by Curriculum... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
Our new app for iPad and iPhone
1 Nov 2017  6:41 amWe’ve just released a new app version of our games for iPad and iPhone. The app is free and it works for existing subscribers, and you can start a subscription (with free trial) within... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
Introducing Bounce for web!
6 Jul 2017  10:25 amWe’ve brought our game Fractions to the web with a new character, a new name, and seven times (!) more levels. Fractions was Motion Math’s first game, and in addition to winning awards such as... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
Playing with Prototypes
11 May 2017  12:27 pmPrototyping is one of the most important stages in the development of Motion Math’s games – the process to get our ideas from paper to something interactive and playable that we can test... [[ This is a content summary only. Visit my website for full links, other content, and more! ]] 
Motion Math is now live on the web!
23 Feb 2017  11:53 am“Can my students play Motion Math on Chromebooks?” That’s the most common question we’ve been asked over the years by teachers. Well, that and “How do you make... [[ This is a content summary only. Visit my website for full links, other content, and more! ]]



MIND Research Institute Blog

New Jersey District Uses ST Math to Foster Productive Struggle
14 Nov 2017  9:00 amEducators know theimportance ofproductive struggle,but the shift to transform math—from worksheets and lectures, to interesting and engaging tasks that enable students to think creatively—doesn't always come easy. Marlboro Township Public Schools developed a districtwide mission to move away from digitized math drills and put students in the mindset to think creatively and build perseverance. Watch the video: ST Math helps students explore nonroutine problems and build number sense instead of memorizing disconnected facts.Interested in learning more about ST Math? Request a 30 day free trial below: 
Profiles in Success: How Mineola Public Schools Prioritized Instruction Over Tests
9 Nov 2017  9:00 amMichael Nagler, Superintendent of Mineola Public Schools, was looking for a way to help his students meet increasingly challenging state standards in math. But he and his team were convinced that more testing was not the right answer. They decided to supplement their K2 curriculum withST Mathto encourage productive struggle and creative problem solving in a lowstakes environment. “In ST Math, the rigor is there but it's not a drillandkill type of program. It's age appropriate and there's a conceptual base that lays the foundation for all future math curriculum.” —Michael Nagler, Superintendent, Mineola Public Schools Mineola educators have seen a huge increase in student engagement... 
Latest in Games and Learning Research Reveals Need to Empower Educators
7 Nov 2017  9:00 amLast month I attended the annual Digital Media and Learning (DML) Conference at University of California, Irvine. DML 2017 was packed with interesting studies and perspectives from education, media and technology researchers from around the world. My schedule of sessions focused on what researchers have learned about games and learning. These four themes emerged from my experience of the conference: <ul> <li>The role of failure in games (and the contrast of the experience of failure in traditional education)</li> <li>The continued importance of experiential learning</li> <li>How the learning experience includes not just the game, but the content and conversions surrounding the game </li> <li>The need to empower teachers to...</li></ul> 
5 Beliefs that Prevent Teachers from Increasing Math Rigor
6 Nov 2017  9:00 amRigor is what moves students into creative and effortful problem solving. It’s the type of learning that challenges, and occasionally frustrates as well. Effective instructional rigor has the power to expand students’ capacity for deeper understanding and intrinsic motivation. However, some common beliefs may be preventing teachers from developing consistently rigorous learning environments. In order to make way for the positive effects of rigor, educators should steer clear of the following assumptions. 1.Direct instruction is enough Students need more than the traditional “I do, we do, you do” model of instruction. Handson, visual experiences can provide all students, regardless of math or... 
New! ST Math Central Resources for Educators
1 Nov 2017  9:00 amSay hello to the new learning hub for ST Math users! ST Math Central provides a tailored experience with new resources, improved navigation and organization, plus a user community. Here's a brief overview of what you can expect to find in ST Math Central. Don't forget to scroll down the page for an exclusive giveaway where you can win a JiJi prize package for you and your classroom just by exploring ST Math Central. How to Access ST Math Central You can bookmarkST Math Central, or click the ST Math Central button on the JiJi Console. When you first login, you'll be prompted to select your grade level(s). This will ensure that you see the most accurate and relevant information for your ST Math...



Ash Tutors

Christmas events for the family in the North West England
2 Nov 2017  3:27 amAre you getting ready to soak up the festive atmosphere this year? If you are, then here is a roundup of some of the best activities, shows and events for the whole family to enjoy this Christmas in the North West and beyond. Some events are extremely popular and you will need to book in advance to avoid disappointment. 
Interesting facts about Halloween
9 Oct 2017  9:55 amReading time 4 minutes. As Halloween approaches, learn a little bit more about the celebration. You might be surprised at what you find out! 
Dyslexia and signs to look out for
9 Oct 2017  9:53 amReading time 4 minutes.Dyslexia is probably much more common that you would initially imagine, with an estimated 1 in 10 to 20 people in the UK having some degree of dyslexia. 
Top tips for building reading skills
11 Sep 2017  3:21 amReading skills are among the most important and necessary learning skills, and as a parent, you have a huge impact on how quickly your child learns to read. Studies have shown that reading out loud to children on a regular basis produces significant gains in comprehension, vocabulary, and the understanding of words.Reading opens up doors to a whole new world full of knowledge, adventure, culture and diversity.Here are 10 simple yet effective tips to build and improve your child's progress in reading, which will not only develop reading skills but also a curiosity and desire to learn. 
Does your child struggle to make friends?
11 Sep 2017  2:59 amIf you are worried because your child is a bit of a loner and seems shy or reluctant to make friends, there are ways you can help and it's extremely beneficial too because as well as being fun, playing with friends is a way for young children to learn social skills.
