Triangular Numbers (Part I) | |
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Elementary explanation of triangular numbers and Gauss demonstration for the sum of the first 100 natural numbers. | |
Triangular Numbers (Part I) | |
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Elementary explanation of triangular numbers and Gauss demonstration for the sum of the first 100 natural numbers. | |
Triangular Numbers (Part II) | |
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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) | |
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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 | |
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Sigma Notation. Tetrahedral numbers. Pyramidal Numbers. Some relations between them. | |
Summation Telescoping Property | |
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We explain the summation telescoping property and apply it to finding two summations. | |
1, 2, 3 ... Infinity. Mathematical Induction | |
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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) | |
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Prove Inequality using the Method of Mathematical Induction. | |
Mathematical Induction (Part III): | |
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Principle of Strong Mathematical Induction. Fermat's Method of infinite descent. Well Ordering Principle. | |
The Well Ordering Principle | |
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Proving The Well Ordering Principle is equivalent to The Principle of Mathematical Induction. | |
Weaving Numbers | |
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Vedic multiplication or weaving multiplication. Fibonacci's sieve or lattice multiplication.John(Napier) 's Bones multiplication. | |
Are you Having Phun yet? | |
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Introduction to Phun. The new entertaining and extreme fun eductional computer program. Using Phun to explain Math. | |
Dimension 2 | |
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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 | |
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M. C. Escher tells the adventures of two-dimensional creatures who are trying to imagine three-dimensional objects. | |
The fourth dimension | |
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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 | |
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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 | |
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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 | |
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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 | |
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The mathematician Heinz Hopf describes his fibration. Using complex numbers he builds beautiful arrangements of circles in space. | |
Fibration continued | |
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The mathematician Heinz Hopf describes his fibration. Using complex numbers he builds beautiful arrangements of circles in space. | |
Proof | |
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Mathematician Bernhard Riemann explains the importance of proofs in mathematics. He proves a theorem on stereographic projection. | |
Pi | |
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Pi, the most famous mathematical constant. | |
