Category Archives: Mathematics

Computationally Fabulous Scarves

Our friend fbz just launched a kickstarter campaign to create algorithmically generated scarves, each one provably unique.

KnitYak scarves ship with the specific code and generating key used to make the pattern on your scarf. There is something powerful about knowing the mathematics and code behind the pattern you are wearing.

She’ll be getting an industrial knitting machine for her company KnitYak to automate the process of manufacturing these individualized creations.

algorithmically generated scarf design

Evil Mad Scientist Valentines: 2015 edition

Lo Res Valentines valentines

For each of the last two years, we’ve released sets of “Download and Print” cards for Valentine’s day. The 2013 set had six equation-heavy cards, and the 2014 set was a set of six symbol-heavy cards.  This year, we’re releasing six new cards, bringing the collection up to a total of 18 cards. This year’s new cards feature love, hearts, and arrows (but no bows or cupids):

My love for you is real

For when your love is complex, but not whatsoever imaginary.

I love you more every day

For that moment when you want to express that not only is the first derivative of your love positive, but so is the second.

Our love is off the charts

(Just in case there was a danger of none of these being sufficiently cheesy.)

You make me glow

Not sure how we missed this one in last year’s set of symbols.  Alternate caption: “You light up my life.”

Solve for i

And what better way to say “I love you,” than with the gift of a math problem?

2015 Evil Mad Scientist Valentines
Lo Res Valentines

You can download the full set here, which includes all 18 designs from the three years (a 765 kB .PDF document).

As usual, print them out on (or otherwise affix to) card stock, and [some steps omitted] enjoy the resulting lifelong romance.

Digi-Comp II replica in Terraria

YouTube user Richard Lewis built a working replica of the Digi-Comp II mechanical computer in the sandbox video game Terraria.

The replica makes extensive use of the so-called “Hoik glitch” in the game, that allows for rapid, controlled player movement, much like gravity guides the balls downward in the original.

More information about the version in Terraria is posted on the video page.

The Power of the Digi-Comp II

Last fall, we built an oversized Digi-Comp II for MIT, which we’ll be posting about in the near future. Today, MIT computer science professor Scott Aaronson published a short “paperlet” about the computational capabilities of the Digi-Comp II on his blog, Shtetl-Optimized:

…it’s amazing that such a simple contraption of balls and toggles could already take us over the threshold of universality.  Universality would immediately explain why the Digi-Comp is capable of multiplication, division, sorting, and so on.  If, on the other hand, we don’t have universality, that too is extremely interesting—for we’d then face the challenge of explaining how the Digi-Comp can do so many things without being universal.

Pi Day is Here

Or, if you prefer, we’re halfway (well, 44% of the way) to Tau day, 6/28.  A fine day to watch the Vi Hart‘s Anti-Pi Rant. And, a fine day to round up some of our finest Pi, Pie, and mathematics projects:

Pi Blanket   Apple Pie

Pi blanket for Pi Day, and the Apple Apple Pie!

 

Earrings 2   Sierpinski Cookies-11

Sierpinski triangles out of polymer clay, and fractal cookies.

Fractal Snowflake Cupcakes - 24 fabric klein bottle

Fractal snowflake cupcakes, Fabric Klein bottle

Snowflake generator SymmetriSketch 2
Vector Snowflake generator application, and Symmetrisketch— for exploring other symmetries.

Christmas fractalSconic Sections
Christmas Chaos and Sconic Sections

Marking Klein Bottles with the Eggbot

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We were lucky enough to have a visit from Cliff Stoll, geek celebrity and proprietor of Acme Klein Bottle. Acme is the finest source of Klein bottles on the internet.

Cliff came with an esoteric dilemma: how to engrave a glass Klein bottle. Acme Klein bottles are blown from borosilicate (Pyrex) glass, which has a low coefficient of thermal expansion, which means that the usual way of engraving a curved glass surface—laser engraving—doesn’t actually work.  With more common types of glass, you can use a laser engraver to etch anything you want into the surface. But with Pyrex, the surface simply melts unevenly rather than creating the microfractures that give an etched appearance.

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So how would you etch the curved surface of a Klein bottle? It turns out, to our surprise, that it is remarkably easy to do it with an Ostrich Eggbot fitted with a diamond engraver attachment.

There was one complication, which is that a Klein bottle is a funny shaped object! In order to fixture the Klein bottle in the Eggbot, we made a couple of extra large couplers—much larger than the tiny pads normally used to hold the ends of an egg—with EVA foam rubber pads on their surfaces. The extra large couplers held the Klein bottle securely for rotation.

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We did some initial tests with Sharpie and a medium sized Klein bottle to make sure our fixturing worked well.

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And then we hooked up an engraver for a real test.

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Here’s what the Klein bottle looked like after engraving. Not being particularly creative, we etched the word “KLEIN” into the side.  Because the Klein bottle is made from thick borosilicate glass, it takes engraving remarkably well. It is a much more sturdy object than the fragile Christmas ornaments that we have engraved in the past.

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While we can’t imagine that it is a major market segment, the Eggbot seems to be ideal for working with Klein bottles (insomuch as anything can be perfect for working with a closed, non-orientable, boundary-free manifold). But regardless, it’s quite wonderful to find an unexpected application like this, where our little robot can solve a real-world problem that we had never even considered.