matematicas visuales visual math


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 You can see more of his works in Do not miss his Stick Figure Museum.

The contents of MatematicasVisuales has been developed by Roberto Cardil.

matematicasVisuales has a page in Facebook. If you likes this site, go into and share matematicasVisuales.

Loci has published my article Kepler:The volume of a wine barrel. Loci is a publication of the Mathematical Asociation of America (MAA). It is the journal of the Matematical Science Digital Library (MathDL). Thanks to Janet Beery, editor of Loci, for her help and encouragement. They has also choosen Taylor Polynomials - Exponential Functions as a resource in his Course Communities in Undergraduate Mathematics.
The Math Forum @ Drexel maintains an Internet Mathematics Library and they have chosen MatematicasVisuales as Hot Spot for the month of August, 2010.
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.
This site matematicasVisuales has been linked as an online resource in The Electronic Journal of Mathematics and Technology. (September, 2012)

12th January 2015

Analysis: Piecewise Functions
Piecewise Linear Functions. Only one piece | matematicas visuales
As an introduction to Piecewise Linear Functions we study linear functions restricted to an open interval: their graphs are like segments.

1st December 2014

Analysis: Piecewise Functions
Piecewise Constant Functions | matematicas visuales
A piecewise function is a function that is defined by several subfunctions. If each piece is a constant function then the piecewise function is called Piecewise constant function or Step function.

27th October 2014

Geometry: Polyhedra
Cube, octahedron, tetrahedron and other polyhedra: Taller de Talento Matemático Zaragoza,Spain, 2014-2015 (Spanish) | matematicas visuales
Material for a sesion about polyhedra (Zaragoza, 7th November 2014). We study the octahedron and the tetrahedron and their volumes. The truncated octahedron helps us to this task. We build a cubic box with cardboard and an origami tetrahedron.

20th October 2014

Geometry: Polyhedra
Resources: Building polyhedra gluing faces  | matematicas visuales
Using cardboard you can build beautiful polyhedra cutting polygons and glue them toghether. This is a very simple and effective technique. You can download several templates. Then print, cut and glue: very easy!

6th October 2014

Geometry: Polyhedra
Chamfered Cube | matematicas visuales
You can chamfer a cube and then you get a polyhedron similar (but not equal) to a truncated octahedron. You can get also a rhombic dodecahedron.

7th July 2014

Geometry: Polyhedra
Truncations of the cube and octahedron | matematicas visuales
When you truncate a cube you get a truncated cube and a cuboctahedron. If you truncate an octahedron you get a truncated octahedron and a cuboctahedron.

2nd June 2014

Geometry: Polyhedra
Truncated tetrahedron | matematicas visuales
The truncated tetrahedron is an Archimedean solid made by 4 triangles and 4 hexagons.

27th April 2014

Geometry: Building Polyhedra, cuboctahedron and rhombic dodecahedron (Spanish)
Construcción de poliedros. Cuboctaedro y dodecaedro rómbico: Taller de Talento Matemático de Zaragoza 2014 (Spanish) | matematicas visuales
Material for a sesion about polyhedra (Zaragoza, 9th May 2014). Simple techniques to build polyhedra like the tetrahedron, octahedron, the cuboctahedron and the rhombic dodecahedron. We can build a box that is a rhombic dodecahedron.

7th April 2014

History: Leonardo da Vinci
Leonardo da Vinci: Drawing of a truncated tetrahedron made to Luca Pacioli's De divina proportione. | matematicas visuales
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the truncated tetrahedron.

3rd March 2014

Analysis: Rational Functions
Rational Functions (4): Asymptotic behavior | matematicas visuales
You can add a polynomial to a proper rational function. The end behavior of this rational function is very similar to the polynomial.

3rd February 2014

Analysis: Rational Functions
Rational Functions (3): Oblique Asymptote | matematicas visuales
For large absolute values of x, some rational functions behave like an oblique straight line, we call this line an oblique or slant asymptote.

7th January 2014

Analysis: Rational Functions
Rational Functions (2): degree 2 denominator | matematicas visuales
When the denominator of a rational function has degree 2 the function can have two, one or none real singularities.

2nd December 2013

Analysis: Rational Functions
Rational Functions (1): Linear rational functions | matematicas visuales
Rational functions can be writen as the quotient of two polynomials. Linear rational functions are the simplest of this kind of functions.

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