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Elementary explanation of triangular numbers and Gauss demonstration for the sum of the first 100 natural numbers.
Using Gauss Idea to find the sum 1+2 + ... +n. Arithmetic progressions an obtaining a general formula for the sum of an arithmetic progression.
Recursive Relation for triangular numbers. Finding a solution to the recursive equation and another solution to the Recursive equation.
Sigma Notation. Tetrahedral numbers. Pyramidal Numbers. Some relations between them.
We explain the summation telescoping property and apply it to finding two summations.
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.
Prove Inequality using the Method of Mathematical Induction.
Principle of Strong Mathematical Induction. Fermat's Method of infinite descent. Well Ordering Principle.
Proving The Well Ordering Principle is equivalent to The Principle of Mathematical Induction.
Vedic multiplication or weaving multiplication. Fibonacci's sieve or lattice multiplication.John(Napier) 's Bones multiplication.
Introduction to Phun. The new entertaining and extreme fun eductional computer program. Using Phun to explain Math.
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?
M. C. Escher tells the adventures of two-dimensional creatures who are trying to imagine three-dimensional objects.
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!
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!
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.
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.
The mathematician Heinz Hopf describes his fibration. Using complex numbers he builds beautiful arrangements of circles in space.
The mathematician Heinz Hopf describes his fibration. Using complex numbers he builds beautiful arrangements of circles in space.
Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem on stereographic projection.
Pi, the most famous mathematical constant.