# ESP Biography

## SACHI HASHIMOTO, ESP Teacher

Major: Mathematics

College/Employer: University of Chicago

## Brief Biographical Sketch:

I'm a sophomore at UChicago. I am very interested in math and teaching math. My other interests include ballet, lindy hop, salsa, and a variety of other forms of dance, art, and American Sign Language.

## Past Classes

(Look at the class archive for more.)

Thinking like a Justice in Splash! 2013 (Nov. 23 - 24, 2013)
Congratulations! You've just been appointed to the Supreme Court. After a long senate confirmation, you've finally got the job, fancy robes and all, and now you get a vote in deciding the Court's next case. But...how is it that you're supposed to decide anyway? Maybe you should read the Constitution? But it's sort of unclear what that old thing says anyway... Well, you'd better look at past cases, right? But if you only followed past cases, the country would never make progress in protecting civil liberties, right? Perhaps you should look at the current public opinion. But...well, that doesn't always jibe with your moral compass, so maybe just vote from the heart? Hm, perhaps this is more complicated than you thought. You suddenly regret not taking that Splash! class on Thinking like a Justice back when you were in high school...

String Theory** in Splash! 2013 (Nov. 23 - 24, 2013)
Let's say you want to hang a picture in your room, and you are worried that the 2,000 fans you bought last week to create the wind tunnel in your room will blow it off the wall, so you want to hang it very securely. You start by wrapping string around some nails in a complicated fashion. You are sure it will be super-duper secure, because you wrapped it around three nails a lot of times. Your mother, angry about the electricity bills from running all your fans, comes over and pulls one of your nails out of the wall ... and your picture comes crashing to the ground! Actually, no matter which nail she removes, it falls! What happened? In this class, you'll be playing with string to solve puzzles like this one, and we'll explore fundamental groups, homology, and monotone boolean functions. **NOT actual string theory. The theory of strings. If you want actual physics-y 11 dimensional string theory, this is not the right class.

The Commerce Clause in Splash! 2012 (Nov. 17 - 18, 2012)
The Supreme Court made headlines this year for its decision in upholding the Affordable Care Act. It upheld the act's individual mandate, a mandate that requires almost all Americans to buy health insurance, on the basis that the government has the power to tax. The government's primary argument in support of the individual mandate was based on the commerce clause: a clause in the US constitution that says Congress has the power "to regulate Commerce with foreign Nations, and among the several States, and with the Indian tribes." Why and how was the government arguing that health care is a form of commerce? What precedent did it have, and how strong was its argument? Why did the Court reject this argument? What could consequences of the Court's decision be in future cases? In the first hour, we will examine the history of the commerce clause and how it came to be used to justify much of the last 70 years of legislation. In the second hour, we will talk about how it relates to the Affordable Care Act, and why the Court's decision was a brilliant political maneuver.

Constitutional Intrigue in Splash! 2012 (Nov. 17 - 18, 2012)
The year was 1800, and Democratic-Republican Thomas Jefferson had just defeated Federalist John Adams in the presidential election. Adams only had a few weeks before Jefferson would take office, and so the Federalist-controlled Congress went to work, swiftly passing new legislation that would allow Adams to appoint new Federalist judges. John Marshall was to deliver the commissions the new judges, but time was too short and some went undelivered. William Marbury, one of the men who did not receive his commission, brought his case to the Supreme Court, of which Marshall was also the Chief Justice, arguing that he had a right to his commission, and asking the Court to order Jefferson to give it to him. What was Marshall to do? On the one hand, if the newly established Supreme Court were to order Jefferson to give the commission to Marbury, it would likely be humiliated by Jefferson's refusal. On the other hand, he wanted both the Federalists and the Supreme Court to have more power in the government. --- Take this class to find out how Marshall brilliantly handled the most dramatic case the Supreme Court has faced. Come learn the story of how the Supreme Court established itself and gained the power to interpret the Constitution and review acts of Congress.

Organized Chaos! in Splash! 2012 (Nov. 17 - 18, 2012)
From just a few simple rules comes an entire universe of possibilities in which we can create a fully functioning computer, self reproducing objects, infinitely expanding patterns, space ships, gliders, and more. This class is about the magic and the math that is Conway's Game of Life. Come learn what it's all about, and be a part of the largest human simulation of the Game of Life!

Proving things with Dots and Lines in Splash! 2011 (Nov. 19 - 20, 2011)
Imagine we have some dogs, and some people who want to adopt dogs. Each person only likes some of the dogs, and each dog only gets along well with some of the people. Can we find a way of matching each person up with a dog, such that everyone is happy? The capital of East Prussia until 1945 was a city called Königsberg. In Königsberg there were several islands connected to each other by bridges. If I give you a drawing of the islands and bridges, can you tell me how to travel across Königsberg using each bridge just once? To answer to these questions and more like them, we turn to a field of mathematics called graph theory. Using dots and lines that join the dots we can come up with ways of talking mathematically about these problems. We will go through the basic theory, definitions, and prove some classic theorems about graphs, dogs and dog owners, cities and bridges, utilities, and handshakes by turning problems about things into problems about dots and lines. Note: This is the version of this class for students in grades 9-12. There is another version for grades 7-9.

Latin Squares in Splash! 2011 (Nov. 19 - 20, 2011)
A latin square is a square grid of size $$n$$ by $$n$$ that is filled with numbers 1 through $$n$$ such that each number is in every column and every row exactly once. For example, Sudoku puzzles are a special form of 9 by 9 latin squares with the extra constraint that the 3 by 3 boxes also have each number exactly once. It turns out many questions we can ask about latin squares are extremely hard: even simple things like 'how many different $$n$$ by $$n$$ latin squares are there?' However, we also know a lot of really awesome things about them: If you are given an $$n$$ by $$n$$ square that has $$n-1$$ filled in numbers such that you haven't broken any of the latin square rules, then you can always complete this partially filled in square into a latin square. But perhaps the Coolest Thing Ever, if you like graph theory, is that latin squares are really just graphs in disguise! We are going to talk a lot about latin squares and graph theory, a little bit about open problems, and ultimately try to tackle a lot of really hard but also very interesting problems.

Proving Things with Dots and Lines in Splash! 2011 (Nov. 19 - 20, 2011)
The capital of East Prussia until 1945 was a city called Königsberg. In Königsberg there were several islands connected to each other by bridges. If I give you a drawing of the islands and bridges, can you tell me how to travel across Königsberg using each bridge just once? To answer to these questions and more like them, we turn to a field of mathematics called graph theory. Using dots and lines that join the dots we can come up with ways of talking mathematically about these problems. We will go through the basic theory, definitions, and prove some classic theorems about graphs, cities and bridges, utilities, and handshakes. Note: This is the version of this class for those in grades 7 - 9. There is another version for those in grades 9-12 that is two hours long and assumes more familiarity with proofs.

Salsa with Salsa! in Splash! 2011 (Nov. 19 - 20, 2011)
Come by and learn to salsa dance and eat some chips and salsa.

Advanced Random Awesome Maths (High School Edition) in Splash! 2011 (Nov. 19 - 20, 2011)
Are you advanced? What about awesome? If so than come to this class! We might do some stuff with Euler’s formula, Stirling’s formula, and the Gamma Function or we might do something totally different. Come and find out!

Advanced Random Awesome Maths (Middle School Edition) in Splash! 2011 (Nov. 19 - 20, 2011)
Are you advanced? What about awesome? If so than come to this class! We might do some stuff with Number Theory, Fractals, and Fibonacci or we might do something totally different. Come and find out!

Aperature Science in Splash! 2011 (Nov. 19 - 20, 2011)
Come learn about cameras and make your own camera! The Splash Enrichment Center reminds you that the camera cannot speak. In the event that the camera does speak, the Splash Enrichment Center urges you to disregard its advice. Also, there will be cake. (Thats a lie)

Learn to Tap Dance! in Spark! 2011 (Mar. 12, 2011)
Tap dance is a super-snazzy looking and sounding dance characterized by quick movements of the feet and rhythmic tapping sounds. In this intro class we'll go through some basic technique and learn a few awesome combinations. We may play around with taping/stringing metal washers to our shoes to get a real tap sound, or simply go barefoot.

How to Cut a Cake in Splash! 2010 (Nov. 20 - 21, 2010)
So here's the issue. You and your friends are trying to share a cake. Perhaps it has sprinkles and frosting flowers, and the cake part is made up of different chocolate and vanilla sections, like any delicious cake should be. Your friends all have different preferences. Laura loves the pink frosting flowers, and Paul is on a diet and wants cake with as little frosting as possible. You just want a piece with chocolate cake. How do you divide the cake up so that everyone gets a fair share (what they think is an nth of the cake)? Are there algorithms, and how well do they work? Are there ways in which we can divide it such that no one envies anyone else's piece? Come to this class, and we'll talk about various aspects of fair division, how it works and how it fails.

Human Knots in Splash! 2010 (Nov. 20 - 21, 2010)
Human knot is a game in which people connects hands in random complicated ways and then try to untangle themselves into a circle. In the course of playing this game, participants sometimes realize that the knot they are making is impossible to untangle. In fact, there are a ton of knots that are impossible to untangle, and in this seminar we will be trying to construct as many as we can. As an extra challenge, we will also see if we can make knots with as few people as possible: did you know the simplest knot, the trefoil, can be made by just one (flexible) person? Come learn about what a knot is, help make some huge knots, break the current bounds on the number of people it takes to make them. (Note: You should be comfortable with being up close with other people, as this involves holding hands and tangling yourselves into knots.)

The Symmetries of Things in Splash! 2010 (Nov. 20 - 21, 2010)
How many ways can I rotate a tetrahedron? How many ways can four people stand in line? What do these questions have to do with each other? In this class we will take a look at the symmetries of objects. This will be an introduction to the field of group theory. You already know a bunch of groups, like the real numbers, polynomials, and modular arithmetic, without even realizing that they're groups. We'll talk about what kind of structure all of these groups have, and what kind of structure more unfamiliar groups have-- like the rotations and reflections of polygons. We will also be using Cayley graphs to visualize this symmetry and get a feel for what the structures are. If you like playing with different systems of rules, if you would like to twist the idea of multiplication, define new notions of addition, and learn with some very awesome math, take this class.

Symmetry and the Complex Plane in HSSP Spring 2010 (Apr. 17, 2010)
The complex plane, the plane that consists of all imaginary numbers, is really a sphere when you patch up a little hole in it. And we can describe functions on the complex plane as movements of the sphere, turning complex algebraic formulas into simple geometric explanations. This class will study some of these movements of the sphere. We'll talk about the mathematics turning a circle inside-out, and pairing two circle and turning them both inside-out at the same time. We'll find some weird symmetry and many beautiful images along the way.

Geometry, Topology, and the Fourth Dimension in Splash! 2009 (Nov. 21 - 22, 2009)
Delve into the mathematics behind how space could be shaped...what if the universe were curved? If we were living on the surface of a fourth dimensional Mobius strip? What does that even mean? We'll talk about universes where if you walk long enough, not only will you end up back where you started, all your writing will look like its mirror image, to everyone else—and everything about them will look like it's been mirrored to you! We'll also look at the complex plane, spheres, and different geometries, and relate that to all of these crazy universes.

Conversational Sign Language in Splash! 2009 (Nov. 21 - 22, 2009)
American Sign Language is a very useful language, whether you're using it to communicate with the Deaf, or with your friends in class. Come learn the basics of sign language and practice signing.

Small Universes in Splash! 2009 (Nov. 21 - 22, 2009)
If I lived on a universe that was connected to itself, I could walk forward and end up where I started. What would it look like if that universe were only as big as a room and I looked up? I could play catch with myself. If it were twisted, even more weird stuff happens. Find out more in this class.

ESPetting Zoo in TEST (2012)
Do you like petting? What about zoos?