Author Archives: Anna Weltman

20

May. ’12

Line Fractals, Knitting, and 3-D Design

Welcome to this week’s Math Munch!

Take a look at this beautiful line drawing:

Jason Padgett

This is called, “Towards Pi 3.141552779 Hand-Drawn,” and it’s by mathematician and artist Jason Padgett.  Jason wasn’t always a mathematician or an artist.  In fact, it was only after a severe head injury that Jason suddenly found that he “saw” fractals and other geometric images in mathematical and scientific ideas.  Jason is interested in limits.  The picture above, for example, is Jason’s artistic interpretation of a limit that approaches pi.  If you draw a circle with radius 1 and make polygons inside of it using secants for their sides, the areas of the polygons get closer and closer to pi as the number of sides increases – but always stay less than pi.  If you take that same circle and make polygons around it using tangents for their sides, the areas of the polygons also get closer and closer to pi as the number of sides increases – but always stay larger than pi.  Jason tried to draw the way that those sequences “trap pi” in this picture.

I think it’s really amazing that Jason draws these by hand.  Here’s some more of Jason’s artwork, and a video of Jason drawing “Towards Pi 3.141552779 Hand-Drawn.”

Space Time Sine Cosine and Tangent Waves

The Power of Pi

Wave Particle Duality
[youtube http://www.youtube.com/watch?v=uHqRTtnU8Wg&feature=fvwrel]

Next, did you like Sondra Eklund’s sweater from last week?  Did it inspire you to do some mathematical knitting of your own?  If so, check out the website Woolly Thoughts.

Woolly Thoughts is run by “mathekniticians” Pat Ashforth and Steve Plummer who love to do, teach, and share math with others through their knitting.  They’ve designed many beautiful and mathematical afghan and pillow patterns, and some patterns for interesting math toys.  Here are some of my favorites:

The “Finite Field” afghan is a color-coded addition table using binary.

The “Fibo-Optic” afghan is made to look like a flying cube using side-lengths based on the Fibonacci sequence.

Finally, one of the programs featured in the new Math Art Tools link is TinkerCAD.  TinkerCAD is a program you can use to make 3D designs – just because, or to print out with a 3D printer!

TinkerCAD has three parts: Discover, Learn, and Design.  In the Discover section, you can browse things that other tinkerers have made and download them to print yourself.  There are some really cool things out there, like this Father’s Day mug made by Fabricatis and this sail boat made by Klyver Boys.

Next, in the Learn section, you can play different “quests” to hone your TinkerCAD skills.  Finally, in the Design section, you can make your own thing!  TinkerCAD is really intuitive to use.  The TinkerCAD tutorial video is really helpful if you want to learn how to use TinkerCAD – as are the quests.

Stay tuned for pictures of some TinkerCAD things made by friends of Math Munch!

Bon appetit!

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29

Apr. ’12

Polyominoes, Rubix, and Emmy Noether

Welcome to this week’s Math Munch!

Check out the Pentomino Project, a website devoted to all things about polyominoes by students and teachers from the K. S. O. Glorieux Ronse school in Belgium.

Their site is full of lots of useful information about polyominoes, such as what the different polyominoes look like and how they are formed.

In this puzzle, place the twelve pentominoes as "islands in a sea" so that the area of the sea is a small as possible. The pentominoes can't touch, even at corners. Here's a possible solution.

Even more awesome, though, is their collection of polyomino puzzles – about dissections, congruent pieces, tilings, and more!  They have a contest every year  – and people from around the world are encouraged to participate!  If you solve a puzzle, you can send them your solution and they might post it on their site.

Next, have you ever thought to yourself, “Gee, I wonder if I can make my own Rubix Cube?”  Well, sixth grader August did just that.  And, after several days of searching for patterns and working hard with paper, scissors, string, and tape, August succeeded!  His 2-by-2 Rubix Cube works just like any other, is fun to play with, and – even better – was fun to make.

Try it yourself:

Finally, ever heard of Emmy Noether?  It’s not surprising if you haven’t, because, according a New York Times article about her, “few can match in the depths of her perverse and unmerited obscurity….”  But, she was one of the most influential mathematicians and scientists of the 20th century – and was named by Albert Einstein the most “significant” and “creative” woman mathematician of all time.  You can read about Emmy’s influential theorem, and her struggles to become accepted in the mathematical community as a Jewish woman, in this article.

Want to learn more about women mathematicians throughout history?  Check out this site of biographies from Agnes Scott College.

Bon appetit!

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02

Apr. ’12

Impossible, Impossible, Impossible

Welcome to this week’s Math Munch!

The Penrose Triangle is an “impossible figure” – or so claim many reputable mathematics sources.  It’s a triangle made of square beams that all meet a right angles – which does sound pretty impossible.  Penrose polygons features in some of M. C. Escher’s most confounding artwork, like this picture:

But, little do these mathematicians know… you can build your own Penrose Triangle out of paper!  Check out these instructions and confound your friends.

Want more optical illusions?  Check out these awesome ones by scientist Michael Bach.

Mathematicians also seem pretty sure that .99999999…. = 1.  Well, trust Vi Hart to show them what’s-what.  Here’s a video in which she tells us all that, in fact, .99999999999… is NOT 1.

Finally, did you know that 13×7=28?  Well, it does.  And here’s the proof:

Bon appetit!  Oh – and April Fools!

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