Maths Ninja, Folding Fractals, and Pi Fun

Welcome to this week’s Math Munch!

ninjaFirst up, have you ever been stuck on a gnarly math problem and wished that a math ninja would swoop in and solve the problem before it knew what hit it?  Have you ever wished that you had a math dojo who would impart wisdom to you in cryptic but, ultimately, extremely timely and useful ways?  Well, meet Colin Beverige, a math (or, as he would say, maths) tutor from England who writes a fun blog called Flying Colours Maths.  On his blog, he publishes a weekly series called, “Secrets of the Mathematical Ninja,” in which the mathematical ninja (maybe Colin himself?  He’s too stealthy to tell)  imparts nuggets of sneaky wisdom to help you take down your staunchest math opponent.

colin_bridgeFor example, you probably know the trick for multiplying by 9 using your fingers – but did you know that there’s a simple trick for dividing by 9, too?  Ever wondered how to express thirteenths as decimals, in your head?  (Probably not, but maybe you’re wondering now!)  Want to know how to simplify fractions like a ninja?  Well, the mathematical ninja has the answers – and some cute stories, too.  Check it out!

A picture of the Julia set.

A picture of a Julia set.

Next, I find fractals fascinating, but – I’ll admit it – I don’t know much about them.  I do know a little about the number line and graphing, though.  And that was enough to learn a lot more about fractals from this excellent post on the blog Hackery, Math, and Design by Steven Wittens.  In the post How to Fold a Julia Fractal, Steven describes how the key to understanding fractals is understanding complex numbers, which are the numbers we get when we combine our normal numbers with imaginary numbers.

complex multiplicationNow, I think imaginary numbers are some of the most interesting numbers in mathematics – not only because they have the enticing name “imaginary,” but because they do really cool things and have some fascinating history behind them.  Steven does a really great job of telling their history and showing the cool things they do in this post.  One of the awesome things that imaginary numbers do is rotate.  Normal numbers can be drawn on a line – and multiplying by a negative number can be thought of as changing directions along the number line.  Steven uses pictures and videos to show how multiplying by an imaginary number can be thought of as rotating around a point on a plane.

here comes the julia set

A Julia set in the making.

The Julia set fractal is generated by taking complex number points and applying a function to them that squares each point and adds some number to it.  The fractal is the set of points that don’t get infinitely larger and larger as the function is applied again and again.  Steven shows how this works in a series of images.  You can watch the complex plane twist around on itself to make the cool curves and figures of the Julia set fractal.

Steven’s blog has many more interesting posts.  Check out another of my favorites, To Infinity… and Beyond! for an exploration of another fascinating, but confusing, topic – infinity.

Finally, a Pi Day doesn’t go by without the mathematicians and mathematical artists of the world putting out some new Pi Day videos!  Pi Day was last Thursday (3/14, of course).  Here’s a video from Numberphile in which Matt Parker calculates pi using pies!

In this video, also from Numberphile, shows how you only need 39 digits of pi to make really, really accurate measurements for the circumference of the observable universe:

Finally, it wouldn’t be Pi Day without a pi video from Vi Hart.  Here’s her contribution for this year:

Bon appetit!

18 responses »

  1. that’s amazing how you use pies to get pie. That was a close estimate when you divided 264 into diameter. thanks for this incredible video.

  2. Wow! This video was so amazing, and I couldn’t stop watching all throughout the video!
    I’ve always loved Pi (the number), and it was so cool to learn that you could use a circle to measure Pi, and to use pies to do it. It’s amazing that that guy got so close to Pi that all he had to do was round to the nearest hundredth! Thank you for this amazing video math munch!

  3. I believe that singing way is a good way to remember the numbers of pie. Does the pie numbers go on forever? How do you still remember all those numbers even when you are singing?

    • Hi Michelle! Singing is a great idea – songs help me remember things, too. The digits of pi do go on forever – and they don’t have a pattern, so that makes them even more difficult to memorize! I bet you’d have to practice a lot to really memorize a lot of digits, but maybe the song would help.

  4. I liked the video of Vi Hart singing the digits of Pi. It must have taken her a long time to remember it. I think singing the way she did would be a easier way of remembering Pi. I would if she could have gone longer than she did.

  5. The video of Vi Hart singing the digits of Pi was really interesting to me. I am a singer, and I can’t recite past 3.14 for Pi. I bet doing this, however would help a lot, especially the way she did different pitches for each digit.

  6. I thought these videos were super cool! Its amazing how people celebrate Pi Day in such differenet ways. My favorite video of the three was when Vi Hart was singing Pi and how she did it in different tones and rythmes. It was also cool how he used pies to calculate Pi and that he got 3.14!!! I had my doubts but it was awesome. 😀

  7. its really cool hoe he used pies to calculate Pi and he actually got 3.14 I also thought it was clever of Vi Hart to turn number of Pi into music notes

  8. These videos were amazing and creative. Vi Hart is an intelligent, witty girl. I really liked how she changed the digits of Pi into different tones, and used real pies to to calculate Pi.

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