In MatematicasVisuales you will find visual expositions of mathematical concepts.
MatematicasVisuales intends to complement the work initiated by artiludios, a site with games, puzzles and mathematical curiosities.
Reading Miguel de Guzmán I found a demonstration of the line of Simpson and the Steiner Deltoid. It serves as an introduction to the geometry section.
The concept of function and its graphical representation are a key concept and we dedicate special attention to it in the analysis section.
Geometric representation of the complex numbers facilitates its visualization. The representation of complex functions usually needs dimension fourth. Sometimes, this difficulty is avoided using colors with which useful and attractive representations are obtained.
Thinking in who have to start learning probability we have this section about this subject.
In the history section we approach mathematics through its history. I try to present the origin and growth of some mathematical concepts.
Miguel Cardil made the design of matematicasvisuales.com. You can see more of his works in www.mcardil.com. Do not miss his Stick Figure Museum.
The contents of MatematicasVisuales has been developed by Roberto Cardil.
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This site MatematicasVisuales has been selected in 2009/11/16 as a "Cool Math Site of the Week"
in the project "Knot a Braid of Links" of the
Canadian Mathematical Society. It is Knot 374.
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NEW February 2010
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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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NEW January 2010
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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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NEW January 2010
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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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NEW December 2009
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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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NEW November 2009
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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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NEW November 2009
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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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NEW October 2009
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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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NEW October 2009
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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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NEW October 2009
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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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NEW September 2009
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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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NEW September 2009
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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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NEW September 2009
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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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NEW June 2009
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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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NEW May 2009
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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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NEW May 2009
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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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NEW February 2009
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New version, developed in Flash, that shows how to calculte the volume of a regular dodecahedron.
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NEW January 2009
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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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NEW January 2009
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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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NEW January 2009
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Gamma, Euler's constant
Euler's constant is defined as a convergent series.
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