## Triangular Numbers (Part I) | |
---|---|

Elementary explanation of triangular numbers and Gauss demonstration for the sum of the first 100 natural numbers. |

## Triangular Numbers (Part II) | |
---|---|

Using Gauss Idea to find the sum 1+2 + ... +n. Arithmetic progressions an obtaining a general formula for the sum of an arithmetic progression. |

## Triangular Numbers (Part III) | |
---|---|

Recursive Relation for triangular numbers. Finding a solution to the recursive equation and another solution to the Recursive equation. |

## It's all Greek to me! Sigma notation | |
---|---|

Sigma Notation. Tetrahedral numbers. Pyramidal Numbers. Some relations between them. |

## Summation Telescoping Property | |
---|---|

We explain the summation telescoping property and apply it to finding two summations. |

## 1, 2, 3 ... Infinity. Mathematical Induction | |
---|---|

Explain the Method of Mathematical Induction. Francesco Maurolico, Pascal and John Wallis. Applying the method of Induction to prove the sum of odd numbers is a square. |

## Mathematical Induction (Part III): | |
---|---|

Principle of Strong Mathematical Induction. Fermat's Method of infinite descent. Well Ordering Principle. |

## The Well Ordering Principle | |
---|---|

Proving The Well Ordering Principle is equivalent to The Principle of Mathematical Induction. |

## Weaving Numbers | |
---|---|

Vedic multiplication or weaving multiplication. Fibonacci's sieve or lattice multiplication.John(Napier) 's Bones multiplication. |

## Are you Having Phun yet? | |
---|---|

Introduction to Phun. The new entertaining and extreme fun eductional computer program. Using Phun to explain Math. |

## Dimension 2 | |
---|---|

Hipparchus explains how two numbers can describe the position of a point on a sphere. He then explains stereographic projection: how can one draw a picture of the Earth on a piece of paper? |

## Dimension three | |
---|---|

M. C. Escher tells the adventures of two-dimensional creatures who are trying to imagine three-dimensional objects. |

## The fourth dimension | |
---|---|

Mathematician Ludwig Schläfli talks to us about objects in the fourth dimension and shows us a procession of regular polyhedra in dimension 4, strange objects with 24, 120 and even 600 faces! |

## The fourth dimension continued | |
---|---|

Mathematician Ludwig Schläfli talks to us about objects in the fourth dimension and shows us a procession of regular polyhedra in dimension 4, strange objects with 24, 120 and even 600 faces! |

## Complex Numbers | |
---|---|

Mathematician Adrien Douady explains complex numbers. The square root of negative numbers is explained in simple terms. Transforming the plane, deforming pictures, creating fractal images. |

## Complex Numbers continued | |
---|---|

Mathematician Adrien Douady explains complex numbers. The square root of negative numbers is explained in simple terms. Transforming the plane, deforming pictures, creating fractal images. |

## Fibration | |
---|---|

The mathematician Heinz Hopf describes his fibration. Using complex numbers he builds beautiful arrangements of circles in space. |

## Fibration continued | |
---|---|

The mathematician Heinz Hopf describes his fibration. Using complex numbers he builds beautiful arrangements of circles in space. |

## Proof | |
---|---|

Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem on stereographic projection. |