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