2021 JSMCH Seminars

2021 Junior Summer Math Camp (Half-Day) Seminars

Intro by Tim Chase, presented by Texas State Math Club

Topology is a branch of mathematics that deals with organization, position, and relationships between objects in a topological space.  This often involves molding, twisting, or stretching objects from one shape into another, but tearing or gluing are not allowed.  Properties in topology can help explain why things can or cannot happen.  We will show you three interesting topology “magic tricks”, show you how to do them yourself, and explain the mathematics that makes the trick work.

Students will need: several sheets of paper, scissors, pencil/pen/marker, a piece of string/yarn (at least 12 inches long), clear tape.

Supporting Files

Magic Tricks PowerPoint

Knot Trick

A Magically Impossible Hole

Explanation of the Tricks

A tangram is a traditional Chinese puzzle made up of seven shapes, called tans, that can be arranged to form many different designs. A tangram is made up of two big triangles, one medium triangle, two small triangles, one square, and one parallelogram.  While it can be fun to just create interesting designs, (in the 1800s alone when tangrams initially became popular, people came up with more than 6,500 configurations), they are also treated as puzzles, where a player is shown a target shape in outline and attempts to recreate the shape using the seven pieces. We will explore these wonderful mathematical designs and try our hand at them.

Students will need: to access the website https://mathigon.org/tangram

Supporting Files

Tangrams PowerPoint

The Puzzle of the Tangram

Tangrams

Game Theory is a branch of mathematics that is used in a variety of disciplines, including economics, military strategy, politics, and other fields, to analyze competitive situations.  The classic two player kids game of Dots and Boxes is a very easy game to learn, but has some very interesting mathematics behind it.  We will explore this game and try to determine winning strategies or advantages that either player can have over the other.

Students will need: to access the website http://dotsandboxes.org/

Alternate places to play Dots and Boxes at:  UCLA dots and boxes game

Dots & boxes at Math Playground

Supporting Files

Dots and Boxes PowerPoint

Dots and Boxes

One of the most interesting “shapes” to come from topology is the Mobius strip.  Despite its simple appearance and construction, this shape has a lot of deep mathematics behind it.  It is described as a surface having only one side and one edge.  While formally discovered in the mid 1800’s, indications are that it may have been known about from ancient Greek or Egyptian times.  Artists and mathematicians alike have been fascinated by this simply designed, complex object.  We will explore some of its properties and talk about the mathematics that exists behind it – while getting actively involved, cutting this shape apart.

Students will need:  Several strips of paper (about 1 inch wide, 11 inches long), scissors, tape

Supporting File

Mobius Strip Magic

Fractals are never-ending patterns that repeat themselves infinitely at different physical dimensions over and over again.  They are called self-similar, so that when you zoom in on a fractal picture, the same pattern appears again and again.  Fractal patterns are seen in math equations, as well as in nature (such as snowflakes or leaves from a tree, rivers, coastlines, etc.), and some can be generated by a computer calculating a simple equation repeatedly.  We will explore the world of fractals, and design some using an online tool.

Students will need: to access the website: https://www.visnos.com/demos/fractal

Supporting File

Fractals PowerPoint