UCLA Olga Radko Endowed Math Circle

ORMC Meetings • 2022-2023 Academic Year

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For meetings prior to Fall 2022, visit the Circle Archive.

Advanced 1AAdvanced 1BAdvanced 2Advanced 3AMC 10/12 A TrainingAMC 10/12 B TrainingAMC 8 TrainingBeginners 1ABeginners 1BBeginners 1C
Beginners 2ABeginners 2BChess clubIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2B

Students will study the Polybius and Caesar cyphers.


Students will warm up solving an anagram. Then they will study the pigpen and rail fence ciphers.


Students will take one last look at ciphers, solve fun problems of other types, and take a quiz on ciphers.

Handouts: Lesson 10

Students will continue their study of logic.


Students will continue studying math logic.


Students will finish the Intro to Math Logic mini-course and take a quiz. If time permits, they will start a new topic, Lineland.


Students will continue studying various shapes intersecting lines and planes.


Students may possibly start the next topic, Traveling on a Cube, if time permits.


We will cover Chapter 15 -- exploring how objects in a higher number of dimensions look when projected into a smaller number.


We will continue with our study of the mathematics of projection. This week we will study Flatland -- a 2D world, in which 3D shapes appear in projected form.


We will do a recap of lineland and flatland, including a short quiz. Then we will start the next topic, which is inverse operations.


We will discuss the book Flatland. Then we will finish Chapter 18, on inverting operations. If we have time, we start a new Chapter on geodesics (shortest paths) on the cube.


In this class we will study geodesics, also known as shortest paths. In most of our experience shortest paths are straight lines. Given any 2 points there is exactly one shortest path between them. But there are spaces in which shortest paths look very different and for which two point may have two very different shortest paths between them (Ch. 19).


We will review Chapter 19, on shortest paths on a cube that students were able to pre-study for homework. Then we will cover Chapter 20, which is a review of both topics. There will be a short quiz. Time permitting, we will start to look at Egyptian multiplication.


We will finish covering Egyptian multiplication.


We will finish studying Chapter 22, revisiting binary numbers. For our class, it is not necessary for students to have studied this topic before in Beginners 1.


We follow Chapter 23, learning how to multiply numbers that are represented in binary form.


Multiplication is standardly introduced as repeated addition. In this lesson, students will learn that division can be introduced as repeated subtraction.


We will do a short discussion of the relationship between ASCII coding and binary numbers. Then we will review some of the techniques from the last two classes (multiplication, division, binary). After a short quiz, we will do some Math Kangaroo problems if time allows.


We will demonstrate and then learn a magic trick that use trinary representations to locate a card in a deck.


Students will continue practicing the trick and discussing the reason it works.


Students will study the associative, commutative, and distributive properties of multiplication using both algebra and geometry.


We discussion arithmetic progressions and their sum formula.


We will start new materials on time. First we will talk about time zones and their relationships to the division of the Earth into meridians. Then, time permitting, we will start to talk about how to do calculations that involve time.

Handouts: handout

Students will start learning basics of mod n arithmetic, that of a circle divided into n equal parts.


We will continue to study the relationship between clocks and arithmetic. Time permitting, we may start our next topic, on the geometry of clocks.


In this class, which will take place over Zoom, we will finish up Clock Arithmetic Part 2, and begin Lesson 27 (Time and Angles).


We will finish our discussion of the relationship between angles and clocks (Lesson 27 - Angles and Time), and then revisit how angles and time on globes.


After a short quiz on clock arithmetic, we will start studying Euclidean geometry.


We will finish our discussion of systems of axioms. Then we will introduce Euclid's postulates for geometry.


We will begin learning Euclidean geometry, starting with Euclid's postulates.

Handouts: handout

Having introduced our definitions in the last class, we will start to learn how to construct and compare triangles using only our straight edge and compasses.

Handouts: handout

We will finish our introduction to Geometry, focusing on using our only available tools to recreate triangles with given dimensions or angle(s). We will practice making rigorous arguments about the properties of


We will do a little geometry practice to reinforce what we've learned in the past three lessons. We will take a quiz. Then we will learn to play some math-games.