Mathigon
Mathigon: Geometry: Polygons and Polyhedra: Tessellations
This lesson focuses on tessellations, a tessellation is a geometric pattern that covers a surface without gaps or overlaps. They can be seen everywhere in nature such as a honeycomb or a tortoise shell.
Mathigon
Mathigon: Geometry: Polygons and Polyhedra: Polyhedra
This lesson focuses on polyhedra; a polyhedron (the plural is polyhedra) is a 3-dimensional solid object that is made up of polygons. Euler's Polyhedron Formula: In every polyhedron, the number of faces (F) plus the number of vertices...
Mathigon
Mathigon: Geometry: Angles and Polygons: Drawing Triangles
This lesson focuses on the Triangle Inequality, when the sum of the lengths of any two sides of a triangle is greater than the length of the third. When this happens, the three sides cannot form a triangle.
Mathigon
Mathigon: Geometry: Triangles and Trigonometry: Triangles Congruence
This lesson focuses on triangle congruence; it shows the ways to prove that triangles are congruent.
Mathigon
Mathigon: Geometry: Triangles and Trigonometry: Pythagoras' Theorem
Pythagoras' Theorem: In any right-angled triangle, the square of the length of the hypotenuse (the side that lies opposite the right angle) is equal to the sum of the squares of the other two sides. (A+B=C)
Mathigon
Mathigon: Geometry: Triangles and Trigonometry: Trigonometry
This lesson focuses on trigonometry including the trigonometric functions: sine, cosine, and tangent.
Mathigon
Mathigon: Geometry: Triangles and Trigonometry: Applications
This lesson focuses on the real world applications using triangles and trigonometry.
Mathigon
Mathigon: Euclidean Geometry: Introduction
Mathematicians in ancient Greece were amazed by mathematical patterns, and wanted to explore and explain them. They began to study mathematics just "for fun" without a specific application in mind. One of these mathematicians, Thales of...
Mathigon
Mathigon: Euclidean Geometry: Euclid's Axioms
This lesson focuses on Euclid's Axioms, simple, intuitive statements, that everyone agrees are true. An axiom(or postulate) is a mathematical statement that is regarded as "self-evident" and accepted without proof. A key part of...
Mathigon
Mathigon: Math Foundations: Divisibility and Primes: Factors and Multiples
This lesson focuses on factors and multiples; it explains each and provides practice activities and a quiz.
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: Casino Mathematics
This lesson focuses on the probability and casino games such as Roulette which consists of a wheel with the numbers from 1 to 36 colored in red and black, as well as a green 0. A ball rolls around the outside and randomly lands on one of...
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: Algebra: Arithmetic and Geometric Sequences
This lesson focuses on arithmetic and geometric sequences using several examples and practice exercises.
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: Circle and Pi: Degrees and Radians
Rather than dividing a circle into some number of segments (like 360 degrees), mathematicians often prefer to measure angles using the circumference of a unit circle - a circle with radius 1. This way of measuring angles is called...