Northern Colorado Math Oval

Click here to go to the main Oval webpage, including a list of upcoming meetings.

### Sunday, April 26, 2015, 2-4 p.m.

**Presenter:**Douglas Ortego

**Title:**Mathematics of Doodling

**Description:**The act of drawing aimlessly can be quite an effective way of helping time move forward in a boring class. But in the spirit of a favorite writer of mine who said everything is interesting to well opened eyes, let's look a lot closer. What does it mean when we use mathematical words like "circular" as adjectives. How do perimeters, areas, and volumes relate to different types of doodles? What kinds of creatures and pictures can we create using simple rules? What kinds of questions and confusions come up when we say something we think is true to someone else?We will have a central question that will be explored in several different directions that revolves around a starting figure and doodles replicating the shape of this figure to a certain extent.

### Sunday, March 22, 2015, 2-4 p.m.

**Presenter:**Josh Maglione

**Title:**Prime numbers help us keep secrets

**Description:**Have you ever wanted to send a message to someone that only they can read? A simple way to scramble a message is to make replacements of each of the letters, but we'll see why this might be a poor choice. Instead, we'll take a more mathematical approach and explore how prime numbers and modular arithmetic play a role in modern message scrambling.

### Sunday, January 25, 2015, 2-4 p.m.

**Presenter:**Steve Ihde

**Title:**Numbers and Sequences: thinking mathematically

**Description:**In this presentation we will discuss some basic number sequences, some simple results about them and some fun little proofs from Paul Erdos. We will then start to take on the task of thinking computationally and try to solve some new problems. An introduction to Project Euler will give us a list of new ideas.

### Sunday, November 23, 2014, 2-4 p.m.

**Presenter:**Mike Mikucki

**Title:**The power of randomness

**Description:**In this presentation, we will investigate what causes small particles to move around even though there seem to be no forces acting on them. This fundamental scientific principle is called diffusion. We'll talk about what diffusion is, act out an example, and come up with a math model. Our math model will open the door to many other exciting discoveries!

### Sunday, November 2, 2014, 2-4 p.m.

**Presenter:**Melissa Adkins

**Title:**The Mathematics of Sudoku

**Description:**

Sudoku is a puzzle that has enjoyed worldwide popularity since 2005. To solve a Sudoku puzzle, one needs to use a combination of logic and trial-and-error. More math is involved behind the scenes: combinatorics used in counting valid Sudoku grids, group theory used to describe ideas of when two grids are equivalent, and computational complexity with regards to solving Sudokus.

### Sunday, October 5, 2014, 2-4 p.m.

**Presenter:**Gavin Polhemus

**Title:**The Geometry of Space-Time

**Description:**We live in a 4-dimensional world, consisting of the three dimensions of space and one time dimension. We will look at some of the surprising similarities between time and space, and as well as the important differences. You will learn how to measure distances in seconds and time in feet. We will do some basic geometry that includes time.

### Sunday, April 27, 2014, 2-4 p.m.

**Presenter:**Professor Alexander Hulpke

**Title:**Cryptography

**Description:**

Since the beginnings of writing mankind has had the desire to write down messages that cannot be read by the uninitiated. The schemes used for this typically relied on replacing letters by other letters in a systematic way. As we will see in the first part, such a scheme is easily broken, in particular if we can guess something about the contents of the message.Modern encryption systems therefore use substitutions that are far less obvious to revert. I will describe the underlying mathematics, modulo arithmetic, and will show how these schemes even allows for seemingly impossible tasks such as secure communication without initially sharing a secret key, electronic signatures (that cannot be copied), digital money, or playing coin toss over the phone.

### Sunday, March 30, 2014 2-4 p.m.

**Presenter:**Sandy Lemberg

**Title:**Special Pi Day Math Oval Event!

**Description:**

If you cannot see the description, please click here.

### Sunday, February 23, 2014, 2-4 p.m.

**Presenter:**Douglas Ortego

**Title:**Famous Families

**Description:**

We will start with counting several ways of combining and recombining a fixed number of objects. This has relations to some very common algebraic situations as well as a nice introduction to recursive problem solving and relating solutions of one problem to seemingly non similar problems. (Clever ways of doing this with somewhat esoteric objects constitutes some of my personal mathematical research.) From here we will discuss new sets of numbers generated by summing the first few of these other numbers. All of this will be explored experimentally at first with dice.

### Sunday, January 26, 2014, 2-4 p.m.

**Presenter: Professor Paul Johnson**

**Title:**Flatland and curved space: an immersion into manifolds

**Description:**

Although we know the earth to be round, just looking nearby us, it appears to be flat. This is an example of what mathematicians call a manifold - something that locally look like n-dimensional space, but twists around back to itself. Similarly, the universe we live in looks like just 3 dimensional space, but perhaps if we flew for trillions of miles in a certain direction in a space ship, we'd come back to earth. We'll give a hands-on introduction to manifolds, and think about what it would be like to live inside of different ones.**Sunday, December 15, 2013, 2-4 p.m.****Presenter:**Prof. James Wilson

**Title:**I dare you to divide by zero!

**Description:**

Ever wanted to divide by zero? Do you think it would be better if a negative times a negative was sometimes negative? Wouldn't it be easier to add fractions without common denominators?Today we will break some of the major rules of math. When you see what happens, you might decide it is better if we follow the rules.

**Sunday, November 10, 2013, 2-4 p.m.****Presenter:**Prof. Mary Pilgrim

**Title:**Hexagons and the aromaticity of benzene molecules

**Description:**

Today we will look at the symmetries of a regular hexagon. We will see how the regular hexagon relates to the benzene molecule as well as what happens with symmetry when we change the benzene molecule. In addition, we will discuss the aromaticity of these changed benzene molecules.

**Sunday, October 20, 2013, 2-4 p.m.****Presenter:**Rachel Neville

**Title:**A Touch of Color

**Description:**

How many many different colors do you need to color a map of the United States? Is there a minimum number of colors that will work for any map? This turns out to be a famous theorem in math. We will look into this problem using tools from graph theory and extend these ideas to problems involving scheduling.

**Sunday, September 22, 2013, 2-4 p.m.****Presenter:**Tim Hodges and Justin Hughes

**Title:**Elementary, My Dear Watson: Introduction to Mathematical Induction

**Description:**

Calculating the sums 1+2, 1+2+3, 1+2+3+4 is easy, but what if we want to know the sum 1+2+3+4+...+999? To calculate this, we would like to find a formula to make it easy. But that's not enough; we also want to prove that our formula is correct.Mathematical induction is one tool which can be used to prove such formulas. In this session, we will define mathematical induction and explore problems which can be solved using induction. We may also address the difference between mathematical induction and inductive reasoning.

**Saturday, 4/27/13, 1-3 p.m.****Presenter**: Anne Ho

**Title**: An exploration of math using origami

**Description**: Origami was traditionally seen as an art form, but in more recent years, it has become viewed as a tool for mathematics and for science. We will explore some activities with connections to number theory, graph theory, geometry, and combinatorics, including Fujimoto's Approximation Technique, PhiZZ units, and folding square twists. We'll also discuss some applications of origami in the scientific world today.

**Saturday, 3/30/13, 1-3 p.m.****Presenter**: Bethany Springer

**Title**: Spirograph math!

**Description**: Once upon a time, a magnificent toy called the spirograph was invented.You played with this toy by anchoring a ring, and then moving a circle along the inside or outside of this ring, drawing crazy curves with beautiful symmetries. In this math oval, we will explore the spirograph and associated historical problems, like the Greek explanation for planetary motion.

**Saturday, 2/23/13, 1-3 p.m.****Presenter**: Douglas Ortego

**Title**: Notions of Space

**Description**: I will talk about different ideas of geometry and try to do something along the lines of a socratic discussion about what geometry "is" and what information we need to study different spaces. Examples will be the surface geometries and objects for observation will be 'triangles', 'polygons' and 'lines of sight' (sorry for my physicist's pedagogical bias).

**Saturday, 1/26/13, 1-3 p.m.****Presenter**: Dr. Mary Pilgrim

**Title**: Patterns in Card Shuffling

**Description**: Mary will lead the group in an investigation about the mathematics of card shuffling. Some math teasers and recreational problems will round out the session.

**Saturday, 12/1/12, 1-3 p.m.****Presenter**: Sandy Lemberg

**Title**: Some challenging geometric, algebraic, probability, and logical conundrums.

**Saturday, 10/20/12, 1-4 p.m.****Presenter**: Dr. Dan Bates

**Title**: When is a knot not a knot? Mathematical notions about "knot theory."

**Saturday, 9/22/12, 1-4 p.m.****Presenter**: Dr. Patrick Shipman

**Title**: Geodesics: When the shortest path between two points is not a straight line.