Mathigon
Mathigon: Geometry: Polygons and Polyhedra: More on Polyhedra
This lesson focuses on polyhedra other than the platonic solids; these include an Archimedean solid, a polyhedron made up of different kinds of regular polygons, that looks the same from every direction. There are 13 different...
Mathigon
Mathigon: Geometry: Circle and Pi: Introduction
This lesson focuses on the characteristics of a circle including similarity, radius, circumference, and Pi. It provides formulas to determine the area of a circle, calculating Pi, and learning exercises throughout.
Mathigon
Mathigon: Probability and Discrete Math: Predicting the Future
This lesson focuses on probability theory for predicting the outcome of flipping a coin, and then flipping it multiple times.
Mathigon
Mathigon: Graphs and Networks: Map Colouring
This lesson focuses on map coloring and the problem of proving that 4 colors would work for all maps. Francis Guthrie had to color a map of counties in England. He observed that four colors seemed to suffice for any map he tried, but he...
Mathigon
Mathigon: Graphs and Networks: The Bridges of Konigsberg
This lesson focuses on developing a way to cross all 7 Bridges of Konigsberg without crossing any of them more than once. Euler discovered it was impossible, but he developed the idea of using graph theory to determine if it would be...
Mathigon
Mathigon: Graphs and Networks: Parties and Dating
This lesson uses handshakes at a party to explain complete graphs, when every vertex is connected to every other vertex. It shows how a formula was created to calculate the number of edges.
Mathigon
Mathigon: Probability and Discrete Math: Monty Hall
This lesson focuses on the Monty Hall game where you select one of three doors. It explains your odds based on your choices.
Mathigon
Mathigon: Probability and Discrete Math: What Are Probabilities
This lesson focuses on probability, a number between 0 and 1 which describes the likelihood of a certain event. A probability of 0 means that something is impossible; a probability of 1 means that something is certain.
Mathigon
Mathigon: Algebra: Special Sequences
In addition to arithmetic and geometric sequences, Fibonacci Numbers, and figurate numbers, there are countless interesting sequences that don't follow a similar, regular pattern. These include prime numbers, perfect numbers, the...
Mathigon
Mathigon: Algebra: Figurate Numbers
There are many other sequences that are based on certain geometric shapes. These sequences are often called Figurate numbers, numbers that can be represented using geometric shapes. Examples include square, triangle, and tetrahedral...
Mathigon
Mathigon: Geometry: Circle and Pi: Conic Sections
The circle is one of four different shapes which can be created using "slices" through a cone, a 3-dimensional solid that has a circular base joined to a single point (called the vertex) by a curved side. If you tilt a cone, you get an...
Mathigon
Mathigon: Geometry: Symmetry
This lesson focuses on symmetry including reflectional symmetry, rotational symmetry, and palindromes. It defines each, gives examples, and practice activities.
Mathigon
Mathigon: Graphs and Networks: Introduction
This lesson provides an introduction to graph theory including directed graphs, disconnected graphs, subgraphs, and order and degrees of a graph.
Mathigon
Mathigon: Probability and Discrete Math: Introduction
This is an introduction to the study of probability. It tells the story of two of the greatest mathematicians, Blaise Pascal and Pierre de Fermat, who used coin tosses of heads or tails to determine who paid the bill. It led to the...
Mathigon
Mathigon: Algebra: Sequences and Patterns
Explore this course in sequences and patterns including simple sequence, triangle and square numbers, terms, recursive formulas, and explicit formulas. Click on Trailer on the top left to watch an introductory video.
Mathigon
Mathigon: Graphs and Networks: The Travelling Salesman Problem
This lesson focuses on the traveling salesman problem which involves finding paths through a city without backtracking. While no algorithm has been found to do that for all cities, there are algorithms that help somewhat. They are...
Mathigon
Mathigon: Geometry: Euclidean Geometry: Definitions
This lesson focuses on Euclidean Geometry terminology; such as line, point, line segment, congruence, circle, radius, ray, and more. It defines each term and provides an example of each.
Mathigon
Mathigon: Geometry: Polygons and Polyhedra: Platonic Solids
A Platonic solid is a polyhedron made up of only one kind of regular polygon, that looks the same from every direction. (In other words, the same number of faces meet at every vertex.) There are only five different Platonic solids:...
Mathigon
Mathigon: Algebra: Fibonacci Numbers
This lesson focuses on Fibonacci numbers, a pattern based on the sum of the two previous numbers. It offers examples and practice exercises using some form of Fibonacci numbers.
Mathigon
Mathigon: Algebra: Sequences: Pascal's Triangle
This lesson focuses on Pascal's Triangle, a number pyramid in which every cell is the sum of the two cells directly above. It contains all binomial coefficients, as well as many other number sequences and patterns.
Mathigon
Mathigon: Probability and Discrete Math: True Randomness
This lesson focuses on randomness; it explains that what we often think of as random is only random because we do not have the tools to make better predictions. However, true randomness does exists -- at the very foundations of matter. A...
Mathigon
Mathigon: Graphs and Networks: Planar Graphs
Here is another puzzle that is related to graph theory. In a small village there are three utility plants producing water, electricity and gas respectively. There are also three houses which need to be served. Unfortunately, due to the...
Mathigon
Mathigon: Graphs and Networks: Euler's Formula
This lesson focuses on Euler's Equation. Any (finite) graph can be constructed by starting with one vertex and adding more vertices one by one. We have shown that, whichever way we add new vertices, Euler's equation is valid. Therefore...
Mathigon
Mathigon: Math Foundations: Divisibility and Primes: Prime Numbers
This lesson focuses on prime numbers, numbers that can only be divided by one and itself. It explains the Fundamental Theorem of Arithmetic and the Sieve of Eratosthenes. Includes practice activities.