MathCandy!

Multiples of consecutive numbers! The columns represent...

Sat, 14 Jul 2012 14:21:00 -0700

Multiples of consecutive numbers! The columns represent integers, and the rows count off on these columns by 2s, 3s, 4s, etc. All sorts of interesting patterns emerge from this! For example, columns with exactly one skittle in them are primes, skittle-rich columns show up a lot in musical harmonics, and diagonal lines which look like these show up in all sorts of places.

Part two! This is an illustration of a neat fact that I noticed a few days ago. Made with mint...

Sun, 08 Jul 2012 17:21:32 -0700

Part two! This is an illustration of a neat fact that I noticed a few days ago. Made with mint patties and licorice. I’m worried that the illustration is a bit opaque, so clarification is below. Just in case.

—Spoiler alert—

Essentially, what I tried to illustrate is this: If you count in binary, starting at 0, (the left column) and at each step tally up the 1s in your number, you get a second sequence: 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, … (the right column). The gif above shows a cool property of this second sequence — to be specific, if you remove every other element, the overall sequence remains unchanged.

Counting in binary with mint patties! Wrapped = 1, unwrapped =...

Sun, 08 Jul 2012 16:20:56 -0700

Counting in binary with mint patties! Wrapped = 1, unwrapped = 0. This isn’t the most original post — I did a similar thing with gummy bears a while back — but I thought it’ll provide a good introduction for my next post, which might otherwise seem kind of opaque.

Parabola! This picture represents a typical definition of a...

Mon, 11 Jun 2012 20:32:16 -0700

Parabola!

This picture represents a typical definition of a parabola: the set of points which are the same distance from a fixed point and a fixed line. Getting the straws right on this one was really difficult, but I’m really happy with the result.

I'm really digging this concept. Math + candy = awesome. Will you be updating anymore?

Mon, 11 Jun 2012 20:05:48 -0700

Thanks! I’ll definitely keep updating. Infrequently, perhaps — it takes a lot of candy to make these, and the half-life of candy in my house is fairly short — but I don’t plan on stopping any time soon.

Frequency count of colors in a random sampling of skittles! Note...

Sat, 21 Apr 2012 22:35:47 -0700

Frequency count of colors in a random sampling of skittles! Note how they’re arranged by descending electromagnetic frequency. I like doing these for various candies — it gives an unusual insight into the marketing side of things. It’s interesting here to note how red is the only outlier in this set. I have a few interesting explanatory hypotheses, but best-guess is that red is just the flavor which people like most. As an aside, this picture was taken in the same cafe where the MathCandy concept started.

This is Bhaskara’s classic first proof of the Pythagorean...

Wed, 01 Feb 2012 18:55:00 -0800

This is Bhaskara’s classic first proof of the Pythagorean Theorem, with dramatic lighting added! I usually use natural light, but due to time constraints I had to get creative here.

Second picture

Buffon’s Needle with Rips licorice, Airheads Xtreme and...

Sat, 21 Jan 2012 17:12:36 -0800

Buffon’s Needle with Rips licorice, Airheads Xtreme and snow! Buffon’s Needle is an interesting problem in geometric probability. Essentially, it asks for the probability that a needle randomly dropped onto a plane of parallel lines will intersect one of the lines.

All of the solutions I know require some calculus, but the solution is really neat—proofs are detailed in the linked article. It turns out that if each line is a needle-length apart, then the probability of the needle intersecting a line ends up being 2/Pi, or roughly 0.6366.

This is an approximation of the Mandelbrot Set using an...

Fri, 28 Oct 2011 01:44:00 -0700

This is an approximation of the Mandelbrot Set using an assortment of brown candies! The hardest part about making this one (and perhaps the reason why it doesn’t have a greater level of detail) was resisting the urge to devour it.

This was a collaboration with the fantastic haiku2! She came up with the concept, helped pick out the supplies and in general did a lot more of the work than I’d like to admit.

This is a hexagonal cellular automaton rendered using Nabisco thin crisps! I planned on doing a...

Thu, 15 Sep 2011 20:38:00 -0700

This is a hexagonal cellular automaton rendered using Nabisco thin crisps! I planned on doing a longer animation, but the details of making it proved harder than I had expected. See if you can figure out the rule!

(Frames: 1, 2, 3, 4, 5, 6, 7, 8, album)

EDIT: Just a heads-up— I made a mistake, so the 7th and 8th frames are actually incorrect. The rest is still good, though!

justaproblem: Nine dots are arranged in a three by three square. Connect each of the nine dots...

Thu, 11 Aug 2011 17:23:00 -0700

justaproblem:

Nine dots are arranged in a three by three square. Connect each of the nine dots using exactly four straight lines and without lifting pen from paper.

Source:Wickelgren, How to Solve Mathematical Problems

Click the image for my solution!

Four iterations of the Sierpinski Triangle, rendered in candy...

Tue, 26 Jul 2011 16:04:00 -0700

Four iterations of the Sierpinski Triangle, rendered in candy corn! Instead of using an iterative approach to building this, I started with the bottom row and built up consecutive rows using an intuitive skipping algorithm, so that it would be easier to position it well on the paper. It was tricky to manipulate and tweak the orientations of the individual candies once the pattern was laid out, but on the whole, I’m really happy with how this turned out.

EDIT: I just found out that this has already been done. I was unaware when I set out to do this, but in the interests of recognizing prior work, a link to the exceptional Vi Hart’s page on this can be found right here!

Circle packing with Pearson’s Mints and Hershey’s...

Mon, 18 Jul 2011 02:18:00 -0700

Circle packing with Pearson’s Mints and Hershey’s Kisses! Picking an angle for this picture was really hard. I ended up picking this close-up shot because it suggests the pattern’s infinite repetition in a way that shots which show a border don’t.

EDIT: Turns out someone uploaded a very nice vector image of this circle packing pattern to Wikipedia! Check it out! If you’re curious, be sure to check the “Other Versions” for different but related circle packing patterns.

WHYHAVEYOUNOTPOSTEDRECENTLY? This is PURE BRILLIANCE

Mon, 11 Jul 2011 18:15:10 -0700

Hey, thanks! :) I was really busy for a while (and also kinda ate most of the candy) so I had to put the project on temporary hold. But now I’m back with plenty of new ideas and I’m starting to establish a buffer so that slowdowns on my end don’t impact the flow of content! I’m shooting for regular updates once or twice a week.

A Riemann sum done with Rips Whips, AirHeads Sour Belts and...

Sun, 10 Jul 2011 20:54:00 -0700

A Riemann sum done with Rips Whips, AirHeads Sour Belts and Junior Caramels for weights! This approximates the integral of sin(x) from 0 to pi. Note that the axes do have the same scale— the green lines indicate the unit length along the x and y axes! Obtaining two lengths with a ratio of 1 to pi so that period of the function could be accurately represented was accomplished with a bit of ingenuity and a glass disk of convenient size.

As an aside, these AirHeads sweetly sour belts are, in total honesty, some of the best candy I have ever had. Most sour candy loses its appeal after the first few tastes, but these not only held up over time remarkably well, but had remarkably intense flavor to boot.

Twizzlers and other stringy things -> Graph theory, knot theory
Candy dots -> Turing machines (à la xkcd)
nonpareils, sweetarts, other round things -> circle packing
ice cream cones -> conic sections
hershey's bars+twizzlers -> riemann integrals

Sun, 26 Jun 2011 20:22:17 -0700

I don’t know who you are, but I like the way you think! I’ll have to try some of these out! I especially like the idea for Riemann integrals — I tried for a while to think of calculus concepts that would lend themselves to candy-renderings, but I wasn’t able to come up with anything. Thanks for the ideas!

Matrix multiplication with jujubes, mike&ikes, a peach ring...

Tue, 03 May 2011 16:57:00 -0700

Matrix multiplication with jujubes, mike&ikes, a peach ring and two sour gummy worm tails! Note that the color-coding simply shows relevant groupings — elements that share a color can still be independent.

The result matrix merits a bit of explanation. If two colors are grouped together, that means that we take the jujube’s row and the mike&ike’s column and multiply together corresponding elements, then add together all the products.

For instance, consider green/red (the second element in the first column of the result matrix): we multiply together the corresponding elements of the green row of jujubes with the red column of mike&ikes, then add together those products. The final result would be g1*r1 + g2*r2 + g3*r3.

I’ve never fully grasped matrices, but after making this I’m inclined to think that matrix multiplication is rather simpler than most explanations of it would lead you to believe.

Rule 30 in licorice! I may or may not have stopped at this point...

Tue, 26 Apr 2011 22:31:00 -0700

Rule 30 in licorice! I may or may not have stopped at this point because I’d been snacking on the black ones to the point where there were none left.

FUN FACT: Even though most of the left half of Rule 30 consists of patterns that are relatively easily recognized and described, the rest of it actually demonstrates mathematically chaotic behavior! Because of this, uses for it in cryptography have been proposed, and Mathematica uses it as one of their random number generation algorithms. Rule 30 is really, really cool.

The Petersen Graph in gummy worms! I wanted to do a 4-coloring...

Tue, 26 Apr 2011 19:35:00 -0700

The Petersen Graph in gummy worms! I wanted to do a 4-coloring of the edges, but it turns out I only have three colors of worms. The vertices can be 3-colored, so if I get some straighter worms, I’m going to try to add jelly beans and illustrate that!

Sequel to the previous picture— counting in base 3 with...

Mon, 25 Apr 2011 03:47:00 -0700

Sequel to the previous picture— counting in base 3 with gummy bears! This took me way longer than it probably should’ve.