Illuminating your mind

### 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 II)

Prove Inequality using the Method of Mathematical Induction.

### 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.

### Pi

Pi, the most famous mathematical constant.

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