28th February 2010
History
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Kepler: The Area of a Circle
Kepler used an intuitive infinitesimal approach to calculate the area of a circle.
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19th February 2010
Complex Functions
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The Complex Cosine Function
The Complex Cosine Function extends the Real Cosine Function to the complex plane. It is a periodic function that shares several properties with his real ancestor.
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5th February 2010
History
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Cavalieri: The volume of a sphere
Using Cavalieri's Principle we can calculate the volume of a sphere.
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13th January 2010
History
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Kepler: Surface and volume of a sphere
Kepler studied the volume and surface of the sphere. He thought the volume of the sphere as made up of small cones, then he sum all of these cones and get a relation between the surface of a sphere en its volume.
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8th January 2010
History
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Kepler: The volume of a wine barrel
Kepler was one mathematician who contributed to the origin of integral calculus. He used infinitesimal techniques for calculating areas and volumes.
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8th December 2009
History
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Kepler: The best proportions for a wine barrel
Studying the volume of a barrel, Kepler solved a problem about maxima in 1615.
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21th November 2009
History
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Mercator and Euler: The Logarithm Function
Mercator published his famous series for the Logarithm Function in 1668. Euler discovered a practical series to calculate.
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16th November 2009
History
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Archimedes' Method to calculate the area of a parabolic segment
Archimedes show us in 'The Method' how to use the lever law to discover the area of a parabolic segment.
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26th October 2009
History, a new section
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Pythagoras' theorem in a tiling
This new section is about Mathematics in his history. We start with Pythagoras' theorem.
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14th October 2009
Complex Functions
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Inversion: an anticonformal transformation
Inversion preserves the magnitud of angles but the sense is reversed. Orthogonal circles are mapped into orthogonal circles.
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6th October 2009
Complex Functions
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Inversion
Inversion is a plane transformation that transform straight lines and circles in straight lines and circles.
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22th September 2009
Complex Functions
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The Complex Exponential Function
The Complex Exponential Function extends the Real Exponential Function to the complex plane.
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14th September 2009
Personal
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In this new version of The Game of Life invented by John H. Conway we can see more than 100 photos of Nature.
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1st September 2009
Taylor polynomials
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Taylor polynomials: Complex Exponential Function
The complex exponential function is periodic. His power series converges everywhere in the complex plane.
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Taylor polynomials: Complex Cosine Function
The power series of the Cosine Function converges everywhere in the complex plane.
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15th June 2009
Taylor polynomials
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Taylor polynomials: Rational function with two real singularities
This function has two real singularities at -1 and 1. Taylor polynomials approximate the function in an interval centered at the center of the series. Its radius is the distance to the nearest singularity.
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Taylor polynomials: Rational function without real singularities
This is a continuos function and has no real singularities. However, the Taylor series approximates the function only in an interval. To understand this behavior we should consider a complex function.
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Taylor polynomials: Rational function with two complex singularities
We will see how Taylor polynomials approximate the function inside its circle of convergence.
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23th May 2009
Taylor polynomials
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By increasing the degree, Taylor polynomial approximates the exponential function more and more.
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By increasing the degree, Taylor polynomial approximates the sine function more and more.
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The function is not defined for values less than -1. Taylor polynomials about the origin approximates the function between -1 and 1.
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The function has a singularity at -1. Taylor polynomials about the origin approximates the function between -1 and 1.
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The function has a singularity at -1. Taylor polynomials about the origin approximates the function between -1 and 1.
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8th May, 2009
Personal, new section
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The Game of Life was invented by John H. Conway. It is one of the most famous bidimensional cellular automaton.
Using a colony we can see some photographs about Nature.
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28th February, 2009
Space Geometry
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New version, developed in Flash, that shows how to calculte the volume of a regular dodecahedron.
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26th January, 2009
Transformations
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Durer
He studied transformations of images, for example, faces.
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The Ambassadors by Holbein the Younger (in Spanish)
In this painting we can see, among lots of interesting things, an anamorphosis of a skull.
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19 January, 2009
Space Geometry
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Volume of a octahedron
The volume of a octahedron is four times the volume of a tetrahedron.
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10th January, 2009
Sequences and Series
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Gamma, the Euler's constant
The Euler's constant is defined as a convergent series.
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8th November, 2008
Space Geometry
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Sections in Howard Eves's tetrahedron
Howard Eves, mathematician and historian of Mathematics, received the George Polya Award for the article
Two Surprising Theorems on Cavalieri Congruence.
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Sections in the sphere
We want to study a surprising Cavalieri congruence between a sphere and a tetrahedron. In this page we can see
sections in a sphere.
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Surprising Cavalieri congruence between a sphere and a tetrahedron
We show a sphere and the Howard Eves's tetrahedron with congruent sections.
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12th August, 2008
Random variables
4th August, 2007
MatematicasVisuales first english version.