matematicasvisuales visual mathematics home

26th July 2010

Geometry
The volume of the tetrahedron (new version) | matematicasvisuales |Visual Mathematics
The volume of a tetrahedron is one third of the prism that contains it.

15th July 2010

Complex Functions
Multifunctions: Powers with fractional exponent | matematicasvisuales |Visual Mathematics
The usual definition of a function is restrictive. We may broaden the definition of a function to allow f(z) to have many differente values for a single value of z. In this case f is called a many-valued function or a multifunction.

11th June 2010

Geometry
The icosahedron and its volume | matematicasvisuales |Visual Mathematics
The twelve vertices of an icosahedron lie in three golden rectangles. Then we can calculate the volume of an icosahedron

7th June 2010

Geometry
Hexagonal section of a cube | matematicasvisuales |Visual Mathematics
We can cut in half a cube by a plane and get a section that is a regular hexagon. Using eight of this pieces we can made a truncated octahedron.
A truncated octahedron made by eight half cubes | matematicasvisuales |Visual Mathematics
Using eight half cubes we can make a truncated octahedron. The cube tesselate the space an so do the truncated octahedron. We can calculate the volume of a truncated octahedron.

2nd June 2010

Analysis
Sum of a geometric series of ratio 1/2 | matematicasvisuales |Visual Mathematics
The geometric series of ratio 1/2 is convergent. We can represent this series using a rectangle and cut it in half successively. Here we use a rectangle such us all rectangles are similar.

25th May 2010

Analysis
Geometric series sum (New Version) | matematicasvisuales |Visual Mathematics
One intuitive example of how to sum a geometric series. In this case, we study the geometric series with ratio equal 1/4.

7th May 2010

Geometry
The truncated octahedron is a space-filling polyhedron | matematicasvisuales |Visual Mathematics
These polyhedra pack together to fill space, forming a 3 dimensional space tessellation or tilling.

28th April 2010

Geometry
Volume of an Octahedron (New Version) | matematicasvisuales |Visual Mathematics
The volume of an octahedron is four times the volume of a tetrahedron. It is easy to calculate and then we can get the volume of a tetrahedron.

23th April 2010

Geometry
The volume of a truncated octahedron | matematicasvisuales |Visual Mathematics
The truncated octahedron is an Archimedean solid. It has 8 regular hexagonal faces and 6 square faces. Its volume can be calculated knowing the volume of an octahedron.

17th March 2010

Complex Functions
The Complex Cosine Function: mapping an horizontal line | matematicasvisuales |Visual Mathematics
The Complex Cosine Function maps horizontal lines to confocal ellipses.

28th February 2010

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

19th February 2010

Complex Functions
The Complex Cosine Function | matematicasvisuales |Visual Mathematics
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
Cavalieri: The volume of a sphere | matematicasvisuales |Visual Mathematics
Using Cavalieri's Principle we can calculate the volume of a sphere.

8th January 2010

History
Kepler: The volume of a wine barrel | matematicasvisuales |Visual Mathematics
Kepler was one mathematician who contributed to the origin of integral calculus. He used infinitesimal techniques for calculating areas and volumes.

8th December 2010

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

21th November 2009

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

16th November 2009

History
Archimedes' Method to calculate the area of a parabolic segment | matematicasvisuales |Visual Mathematics
Archimedes show us in 'The Method' how to use the lever law to discover the area of a parabolic segment.

26th Octuber 2009

History
Pythagoras' Theorem in a tiling | matematicasvisuales |Visual Mathematics
We can see Pythagoras' Theorem in a tiling. It is a graphic demonstration of Pythagoras' Theorem we can see in some floor made using squares of two different sizes.

14th October 2009

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

6th October 2009

Complex Functions
Inversion | matematicasvisuales |Visual Mathematics
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 | matematicasvisuales |Visual Mathematics
The Complex Exponential Function extends the Real Exponential Function to the complex plane.

14th September 2009

Personal
Life Vida (New version, more photos) | matematicasvisuales |Visual Mathematics
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 | matematicasvisuales |Visual Mathematics
The complex exponential function is periodic. His power series converges everywhere in the complex plane.
Taylor polynomials: Complex Cosine Function | matematicasvisuales |Visual Mathematics
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 | matematicasvisuales |Visual Mathematics
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 | matematicasvisuales |Visual Mathematics
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 | matematicasvisuales |Visual Mathematics
We will see how Taylor polynomials approximate the function inside its circle of convergence.

23th May 2009

Taylor Polynomials
Taylor polynomials: Exponential function | matematicasvisuales |Visual Mathematics
By increasing the degree, Taylor polynomial approximates the exponential function more and more.
Taylor polynomials: Sine function | matematicasvisuales |Visual Mathematics
By increasing the degree, Taylor polynomial approximates the sine function more and more.
Taylor polynomials: Square root | matematicasvisuales |Visual Mathematics
The function is not defined for values less than -1. Taylor polynomials about the origin approximates the function between -1 and 1.
Taylor polynomials: Rational function 1 | matematicasvisuales |Visual Mathematics
The function has a singularity at -1. Taylor polynomials about the origin approximates the function between -1 and 1.
Taylor polynomials: Rational function 2 | matematicasvisuales |Visual Mathematics
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
Life Vida | matematicasvisuales |Visual Mathematics
Te 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
Regular dodecahedron | matematicasvisuales |Visual Mathematics
One eighth of a regular dodecahedon of edge 2 has the same volume as a dodecahedron of edge 1.

26th January 2009

Transformations
Durer | matematicasvisuales |Visual Mathematics
He studied transformations of images, for example, faces.
Los Embajadores de Holbein el Joven | matematicasvisuales |Visual Mathematics
In this painting we can see, among lots of interesting things, an anamorphosis of a skull. (In Spanish)

19th January 2009

Space Geometry
Volume of an octahedron | matematicasvisuales |Visual Mathematics
The volume of an octahedron is four times the volume of a tetrahedron. It is easy to calculate and then we can get the volume of a tetrahedron.

10th January 2009

Sequences and Series
Gamma, Euler's constant | matematicasvisuales |Visual Mathematics
Gamma, the Euler's constant, is defined using a covergent series.

17th November 2008

Space Geometry
Regular dodecahedron | matematicasvisuales |Visual Mathematics
One eighth of a regular dodecahedon of edge 2 has the same volume as a dodecahedron of edge 1.
Volume of a regular dodecahedron (Flash version) | matematicasvisuales |Visual Mathematics
One eighth of a regular dodecahedon of edge 2 has the same volume as a dodecahedron of edge 1.

8th November 2008

Space Geometry
The volume of the tetrahedron | matematicasvisuales |Visual Mathematics
The volume of a tetrahedron is one third of the prism that contains it.
Sections on a tetrahedron | matematicasvisuales |Visual Mathematics
Special sections of a tetrahedron are rectangles (and even squares)
Sections in Howard Eves's tetrahedron | matematicasvisuales |Visual Mathematics
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 | matematicasvisuales |Visual Mathematics
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 tetrahedronn | matematicasvisuales |Visual Mathematics
We show a sphere and the Howard Eves's tetrahedron with congruent sections.

12th August 2008

Random Variables
Binomial distribution | matematicasvisuales |Visual Mathematics
When modeling a situation where there are n independent trials with a constant probability p of success in each test we use a binomial distribution.
Poisson distribution | matematicasvisuales |Visual Mathematics
Poisson distribution is discrete (like the binomial) because the values that can take the random variable are natural numbers, although in the Poisson distribution all the possible cases are theoretically infinite.
Normal distribution | matematicasvisuales |Visual Mathematics
The Normal distribution was studied by Gauss. This is a continuous random variable (the variable can take any real value). The density function is shaped like a bell.
One, two and three standar deviations | matematicasvisuales |Visual Mathematics
One important property of normal distributions is that if we consider intervals centered on the mean and a certain extent proportional to the standard deviation, the probability of these intervals is constant regardless of the mean and standard deviation of the normal distribution considered.
Calculating probabilities in Normal distributions | matematicasvisuales |Visual Mathematics
It may be interesting to familiarize ourselves with the probabilities correspondig to different intervals in normal distributions.
T Student distribution (Spanish) | matematicasvisuales |Visual Mathematics
T Student distribution was studied by William Gosset(1876-1937)
Calculating probabilities in t Student distributions (Spanish) | matematicasvisuales |Visual Mathematics

4th August 2007

MatematicasVisuales first English version.