UCLA Olga Radko Endowed Math Circle

ORMC Meetings • 2021-2022 Academic Year

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For meetings prior to Fall 2021, visit the Circle Archive.

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We will solve some cool math puzzles to warm up for the year.

Handouts: Handout

We will study the consequences of basic similar triangles properties

Handouts: Handout

Understanding planetary habitability is key to understanding how and why life developed on Earth as well as whether life is present on planets that orbit different stars (exoplanets). Whether a planet could be habitable is determined primarily by the planet's climate. This lecture will address insights we've gained from studying Earth's climate and how those have been used to make predictions about which exoplanets might be habitable, and how astronomical observations indicate the possibility of new climatic regimes not found on modern Earth. Finally, the lecture will cover some questions about the future of humanity and the Fermi paradox.

Dorian Abbot is an Associate Professor of Geophysical Sciences at the University of Chicago. In his research he uses mathematical and computational models to understand and explain fundamental problems in Earth and Planetary Sciences. Professor Abbot has also worked on problems related to climate, paleoclimate, the cryosphere, planetary habitability, and exoplanets. Recently he's been focusing on terrestrial exoplanets and habitability. He has an undergraduate degree in physics and a PhD in applied math, both from Harvard University.

Handouts: Handout

We have a game! Bring your warrior spirit!

Handouts: Game questions

We will play with frieze patterns, featured in this Numberphile video

Handouts: Handout

We will study what is called "general topology" and is a subject usually taught as an upper-division course to math majors.

Handouts: Handout

We revisit induction and if time allows go to the formalism of Peano axioms

Handouts: Handout

We have a game to mark the end of the quarter


We continue our work with the Peano axioms and induction handout.

Handouts: Handout

We study Cauchy induction, a beautiful modification of the usual induction. If traditional induction goes forward one step at a time, Cauchy jumps from n to 2n and then goes backward if he misses the needed number.

Handouts: Handout

Josephus and his forty soldiers were trapped in a cave. This means that there was a total of 41 fighters in the circle. Let us number 1 the first fighter to raise his sword, let us number 2 the fighter to his right, etc. The goal of this lesson is to solve the following two problems.

Problem 1 What was the position of Josephus in the circle?

Problem 2 Suppose that there are n soldiers, including Josephus, in the cave. What should the position of Josephus be in order for him to stay alive?

Handouts: Handout

We again solve problems regarding the angles in the circle. This is the theme uniquely rich with nice problems.

Handouts: Handout

This time we have a game with our usual rules

Handouts: Game

The first hour will be a lecture by our instructor Natalie and me about hat puzzles. We invited other groups to listen. In the second hour, we will do the attached worksheet on hat puzzles.

Handouts: Handout

We discuss the ways to prove that some numbers are irrational

Handouts: Handout

We continue the last week handout about proving irrationality of certain numbers

Handouts: Handout

End of the quarter game

Handouts: Game

We solve problems leading to information theory.

This handout is inspired by the video by 3Blue1Brown on solving wordle using information theory. youtu.be/v68zYyaEmEA

Handouts: Handout

We will build a model of hyperbolic space!

Special thanks to Professor Frank Sottile for recommending these activities to us.

The material for these activities can be found at https://www.math.tamu.edu/~sottile/research/stories/hyperbolic_football/

Handouts: Handout

We are doing a well-tried handout on pigeonhole principle.

Handouts: Handout

We study the basic number theory needed for secure communication.

Handouts: Handout

We have a game!


We study the beginnings of calculus and the number e=2.71...

Handouts: Handout

This lesson is going online because of COVID. We study binomial coefficients and Pascal triangle -- basic objects in combinatorics.

Handouts: Handout