matematicas visuales visual math

28th February 2010

History
Kepler: The Area of a Circle
Kepler: The Area of a Circle
Kepler used an intuitive infinitesimal approach to calculate the area of a circle.

19th February 2010

Complex Functions
The Complex Cosine Function: A Geometric Approach
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.

5th February 2010

History
Kepler: Surface and volume of a sphere
Cavalieri: The volume of a sphere
Using Cavalieri's Principle we can calculate the volume of a sphere.

13th January 2010

History
Kepler: Surface and volume of a sphere
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.

8th January 2010

History
Kepler: the volume of a wine barrel
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.

8th December 2009

History
Kepler: the best proportions for a wine barrel
Kepler: The best proportions for a wine barrel
Studying the volume of a barrel, Kepler solved a problem about maxima in 1615.

21th November 2009

History
Mercator and Euler: The Logarithm Function
Mercator and Euler: The Logarithm Function
Mercator published his famous series for the Logarithm Function in 1668. Euler discovered a practical series to calculate.

16th November 2009

History
Taylor polynomials: Rational function with two complex singularities
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.

26th October 2009

History, a new section
Taylor polynomials: Rational function with two complex singularities
Pythagoras' theorem in a tiling
This new section is about Mathematics in his history. We start with Pythagoras' theorem.

14th October 2009

Complex Functions
Inversion: an anticonformal transformation
Inversion: an anticonformal transformation
Inversion preserves the magnitud of angles but the sense is reversed. Orthogonal circles are mapped into orthogonal circles.

6th October 2009

Complex Functions
Inversion is a plane transformation that transform straight lines and circles in straight lines and circles
Inversion
Inversion is a plane transformation that transform straight lines and circles in straight lines and circles.

22th September 2009

Complex Functions
The Complex Exponential Function extends the Real Exponential Function to the complex plane
The Complex Exponential Function
The Complex Exponential Function extends the Real Exponential Function to the complex plane.

14th September 2009

Personal
In this new version of The Game of Life invented by John H. Conway we can see more than 100 photos of Nature.

1st September 2009

Taylor polynomials
Taylor polynomials: Complex Exponential Function
Taylor polynomials: Complex Exponential Function
The complex exponential function is periodic. His power series converges everywhere in the complex plane.
Taylor polynomials: Complex Cosine Function
Taylor polynomials: Complex Cosine Function
The power series of the Cosine Function converges everywhere in the complex plane.

15th June 2009

Taylor polynomials
Taylor polynomials: Rational function with two real singularities
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.
Taylor polynomials: Rational function without real singularities
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.
Taylor polynomials: Rational function with two complex singularities
Taylor polynomials: Rational function with two complex singularities
We will see how Taylor polynomials approximate the function inside its circle of convergence.

23th May 2009

Taylor polynomials
By increasing the degree, Taylor polynomial approximates the exponential function more and more.
By increasing the degree, Taylor polynomial approximates the sine function more and more.
The function is not defined for values less than -1. Taylor polynomials about the origin approximates the function between -1 and 1.
The function has a singularity at -1. Taylor polynomials about the origin approximates the function between -1 and 1.
The function has a singularity at -1. Taylor polynomials about the origin approximates the function between -1 and 1.

8th May, 2009

Personal, new section
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.

28th February, 2009

Space Geometry
New version, developed in Flash, that shows how to calculte the volume of a regular dodecahedron.

26th January, 2009

Transformations
Durer
He studied transformations of images, for example, faces.
The Ambassadors by Holbein the Younger (in Spanish)
In this painting we can see, among lots of interesting things, an anamorphosis of a skull.

19 January, 2009

Space Geometry
Volume of a octahedron
The volume of a octahedron is four times the volume of a tetrahedron.

10th January, 2009

Sequences and Series
Gamma, the Euler's constant
The Euler's constant is defined as a convergent series.

17th November, 2008

Space Geometry

8th November, 2008

Space Geometry
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.
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.
Surprising Cavalieri congruence between a sphere and a tetrahedron
We show a sphere and the Howard Eves's tetrahedron with congruent sections.

4th August, 2007

MatematicasVisuales first english version.