# Mathemalchemy

## A minicourse featuring Ingrid Daubechies

October 9, 11, 16, and 18, and November 7, 8, 15, and 17
6:30 pm to 7:30 pm

(in person)

Designed and fabricated during the pandemic by a team of 24 mathematical artists and artistic mathematicians, the Mathemalchemy art installation celebrates the fun, beauty, and creativity of mathematics.  It depicts a magical wonderland where critters of all stripes are surrounded by mathematical objects and observe customs interwoven with mathematics.  At present, Mathemalchemy is touring North America; it can also be explored online at mathemalchemy.org.  The installation illustrates many different subfields of mathematics, and at many different levels.  Join Distinguished Visiting Professor Ingrid Daubechies and delve a little deeper into several of these, exploring both the mathematical concepts and their visualizations in Mathemalchemy.

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### Mathemalchemy: Infinity

Monday, October 9, 6:30 pm
It is easy to start enumerating numbers that go on forever by following a simple rule — mathematicians would call this an infinite sequence.  Examples are 1,2,3,4,5,6,… (where every number is 1 more than the previous one) or 1, 1/2, 1/4, 1/8, 1/16,… (where every number is half of the previous one).  In the first of these examples, the individual numbers become larger and larger; in the second they become smaller and smaller.  The sums of the terms in the first example grow even faster than the numbers themselves (1,3,6,10,15,21,…) while in the second example, these sums never even exceed 2 (1, 3/2, 7/4, 15/8, 31/16,…).  This is an example of a converging series, where a sum of infinitely many terms is nevertheless still finite.  In this first session of the series, encounter more fun examples where infinity plays a role, and get a glimpse of different types of infinity.

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### Mathemalchemy: Symmetric patterns and tiling

Wednesday, October 11, 6:30 pm
There are only so many ways (17, to be precise) in which one can arrange a given pattern on the plane so that it keeps repeating “rhythmically,” as on wallpaper.  In the Mathemalchemy art installation, a little mouse appears all over, illustrating each of these.  But sometimes it is knitted, sometimes embroidered, sometimes appliquéd — why?  Each of these wallpaper arrangements also defines a periodic tiling of the plane, a regular arrangement of the same shape, copied over and over again; together these copies cover the plane exactly, without overlaps.  There also exist non-periodic tilings — how do they work?

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### Mathemalchemy: Error-correcting codes

Monday, October 16, 6:30 pm
We start by playing a game: you pick an arbitrary number between 1 and 16 that I will have to guess.  You have 7 cards, on each of which the numbers 1 through 16 are printed, 8 of them on the yellow front and 8 on the green back.  For each card, I ask whether your special number is on the yellow side or the green side, and you answer — but not necessarily truthfully!  You can choose to lie, but at most once.  At the end, I tell you not only your number, but also whether you lied or not, and for which card!  We will first play the game, and then see why it works.  Underlying this game is an error-correcting code that is illustrated on the Cryptography quilt in the Mathemalchemy installation.

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### Mathemalchemy: Prime and composite numbers

Wednesday, October 18, 6:30 pm
The squirrels and chipmunks in Mathemalchemy are having their annual festival, and are exploring prime numbers.  We’ll look over their shoulders to see what they are doing and try to understand what Tassos the librarian is squirrel-splaining.  And maybe we’ll understand the mysterious mosaic pavers in the park…

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### Mathemalchemy: Self-similarity and fractals

Tuesday, November 7, 6:30 pm
Self-similarity at different scales abounds in the Mathemalchemy art installation: from the Koch snowflakes to the different-sized bees and their hives, or to the decoration of the Bakery roof and Tess’s kite.  These decorations also play a role in understanding nonperiodic tilings!

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### Mathemalchemy: Chaos

Wednesday, November 8, 6:30 pm
Even chaos and chaotic dynamics are illustrated in the Mathemalchemy art installation.  But what does it mean, precisely, to say that some behavior is chaotic?  And do flapping butterflies in the Brazilian rainforest really influence the weather in New York?

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### Mathemalchemy: Polyhedra and their symmetries

Wednesday, November 15, 6:30 pm
Many people are familiar with the platonic solids: the tetrahedron, the cube, the octahedron, the dodecahedron and the icosahedron.  They have beautiful symmetries, and there are some very interesting relationships among them.  You can make other beautiful polyhedra by cutting corners from the platonic solids.  And some of these can even be found in the design of World Cup soccer balls!

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### Mathemalchemy: Proofs without words

Friday, November 17, 6:30 pm
Clearly we shouldn’t use words to explain proofs without words; you’ll just have to come to this presentation to see the examples, some of which are also wonderful graphic designs!

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