# 20 Fascinating Things We Saw At Manhattan’s New Museum Of Mathematics

[credit provider=”Walter Hickey / BI”]

The National Museum of Mathematics opened up December 15th in Midtown, and we had to check it out. It’s two stories packed with hi-tech computers and mathematical experiments that make this museum perfect for anyone from elementary school to a Ph. D program.

It’s really rare that you see a museum that gets it right for every age, but I learned a ton of new things at MoMath.

maths professors and Rubik’s Cube solver clubs hang out there. MoMath has everything from World War Two cryptography equipment to Android-powered exhibits every couple of feet.

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title=”MoMath just opened up on 26th street between Broadway and Fifth Avenue”
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title=”While a lot of the presentation is aimed at school-age kids, a lot of the material is pulled directly out of Grad school level mathematics.”
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title=”1. The centrepiece of the upstairs floor, for example, is the square-wheeled tricycle that actually works”
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title=”Each “wheel” of the tricycles only work on one exact circular path, though, where the length of the arc of the hump is exactly equal to the length of the side of the square. As such, each wheel is a totally different but exactly calibrated size.”
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title=”2. Also on the top floor is a physics experiment where people adjust tracks to try to make a car move fastest down a track”
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title=”While these kids are having fun, they’re also solving the Bachistochrone problem: How do we make the curve of fastest descent between two points?”
content=”Bachistochrone curve
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title=”The answer, first solved by Johann Bernoulli, is an upside down cycloid that leads to quick acceleration, not a single slope that requires accumulated momentum.”
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title=”3. The museum also has a 3D printer to print different curves, surfaces and manifolds”
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title=”The museum has a bunch of different topological printouts”
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title=”The top two are Klein Bottles, a closed surface with no distinction between the inside and outside,”
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title=”4. Spanning two floors is a sculpture, String Product, that goes down the middle of that staircase.”
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title=”Interestingly enough, this is actually a complex calculator”
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[slide
title=”Here’s the slide from MoMath describing the concept.”
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title=”In essence, you find the two points on the outside of the paraboloid that you want to multiply, then locate the string connecting them.”
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title=”It will pass by the pole running up the centre of String Product. The number written there is the solution to the multiplication problem.”
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title=”5. Downstairs, there’s a large section of space devoted to geometric cross sections of three dimensional objects.”
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title=”One exhibit, The Wall of Fire, makes a plane out of lasers that you can use to try to make cross sections of desired shapes.”
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title=”Here’s an elliptical cross section of a cylinder — Cylinders can also be cut into semi-circles, rectangles and circles”
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title=”6. Here’s a square cross section of a pyramid, with some slight enhancements added later by me for clarity.”
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title=”7. Finding the decagon cross section of this dodecahedron was “Wall of Fire hard mode””
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title=”8. This was the feedback fractal exhibit. Each of those mounts has a camera that can be configured into making a fractal.”
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title=”The guy who had the green screen was already really good at this and had a fractal by the time I got there. Notice how he has a self-similar pattern going down into the centre.”
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title=”The trick is to point your camera at a portion of the screen so that it has visual feedback.”
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title=”With a little teamwork we made some fun looking fractals in a few minutes.”
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title=”9. This is a working M-209, the mechanical cypher machine used by the United States throughout World War Two. Cryptographic work done during the early forties the stage for modern computers.”
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title=”Opening up the M-209, it’s an outstandingly complicated device. 140,000 of the devices were built and remained in service through the Korean War.”
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title=”10. The museum has “Enigma Cafe,” designed to have different puzzles like this Iron Heart.”
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title=”Fundamentally, disentanglement puzzles like this are topology problems. Here’s how you solve the Iron Heart.”
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title=”First, get the stem of the heart through the loop.”
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title=”Then, give the bar a twist. The heart will slip right off. Some professors use tavern puzzles like this to explain concepts from topology,”
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title=”11. This exhibit, “sixth sense,” says it will predict the sum of six selected numbers — one from each column, one form each row — accurately.”
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title=”Essentially, this teaches people how to trick others by rigging the numbers. The numbers always add up to 111 when one from each column and each row is selected.”
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title=”12. This is the “Missing Square” puzzle. What happened to the missing square after the rearrangement?”
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title=”Here’s the explanation for the “missing square problem.” The second triangle’s hypotenuse is bent.”
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title=”13. This is the second Penrose Tiling, made up of “kites” and “darts,” both related to the geometry of the pentagon.”
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title=”14. This was one of the more popular exhibits, and attracted several maths professors. The goal was to create a 3D object that, when rolled, would make the paths on the table.”
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title=”The different surfaces could be flipped around to create entirely different objects.”
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title=”For instance, this object I made made the path on the right when rolled.”
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title=”15. This piece allowed the users to try their hand at the tricky most efficient packing problem”
content=”More on packing problems
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title=”The computer would determine the smallest geometric object necessary to bound all of the shapes on the table in the way they are arranged. Even better, it kept track of who held the records for most efficiently packed shapes.”
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title=”With a variety of shapes to choose from — including the “expert difficulty setting” circles — this was a great look into one of the trickiest concepts in geometry.”
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title=”16. This is a visual, geometric proof of the Pythagorean Theorem that anybody could do using the red tiles.”
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title=”The red tiles take up the entire area of the “a” squared and “b” squared.”
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title=”They also take up the entire are of “c” squared. Hence, a0 squared plus b squared equals c squared.”
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title=”The Enigma Cafe naturally had several Rubik’s Cubes, presumably beyond repair at this point.”
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title=”17. While it doesn’t carry to the visual medium well, this exhibit uses chords for each ball to explore the relationship between music and maths.”
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title=”Here’s one of the best parts of the whole museum, the maths Square from Google (a major supporter of MoMath)”
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title=”18. In this mode, the maths Square calculates the Voronoi cell of everyone standing on it”
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title=”The Voronoi cell, named after Georgy Voronoi, is the portion of territory closer to you than anyone else.”
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title=”19. The travelling Salesman problem seeks to calculate the shortest configuration of line segments to connect different points. maths Square calculates the solution in real time.”
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title=”The whole museum has art pieces like these stereograms from Michael Brand called “Light Grooves””
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title=”20. The museum also has an enviable gift shop — Here’s some set theory for you. “U” means Union, “n” mean intersection. So 2 o’clock is represented by the intersection of A and C, which has three dots.”
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title=”Altogether, the Museum of maths is a really cool experience for geeks and maths fans alike. I didn’t know how much fun I was having until I realised I spent three hours there.”
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