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)
Convergence: Where Mathematics, History, and Teaching Interact,is a digital publication of the Mathematical Association of America. In 2022 they published my article Kepler and the Rhombic Dodecahedron. Thanks to the editors of Convergence, Amy Ackerberg-Hastings, Janet Heine Barnett, for their support.

28th February 2022

Tetraxis, a puzzle by Jane and John Kostick | matematicas visuales
Tetraxis is a wonderful puzzle designed by Jane and John Kostick. We study some properties of this puzzle and its relations with the rhombic dodecahedron. We can build this puzzle using cardboard and magnets or using a 3D printer.

7th January 2019

History: Kepler and the volume of a wine barrel (another look)
Kepler: The volume of a wine barrel. Another look | matematicas visuales
Kepler was one mathematician who contributed to the origin of integral calculus. He used infinitesimal techniques for calculating areas and volumes. In this page we study one optimization problem.

12th November 2018

Geometry: Pascal's Theorem
Pascal's Theorem | matematicas visuales
If a hexagon is inscribed in a circle, the three pairs of opposite sides meet in collinear points.

14th May 2018

History: Durer and the ellipse
Albert Durer and ellipses: cone sections. | matematicas visuales
Durer was the first who published in german a method to draw ellipses as cone sections.
Albert Durer and ellipses: Symmetry of ellipses. | matematicas visuales
Durer made a mistake when he explanined how to draw ellipses. We can prove, using only basic properties, that the ellipse has not an egg shape .

7th May 2018

Geometry: Ellipses
Ellipses as sections of cylinders: Dandelin Spheres | matematicas visuales
The section of a cylinder by a plane cutting its axis at a single point is an ellipse. A beautiful demonstration uses Dandelin Spheres.

2nd April 2018

Geometry and History
Leonardo da Vinci:Drawing of an augmented rhombicuboctahedron 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 augmented rhombicuboctahedron.
Leonardo da Vinci:Drawing of an augmented rhombicuboctahedron made to Luca Pacioli's De divina proportione (2). | matematicas visuales
We can see the interior of the augmented rhombicuboctahedron. Luca Pacioli wrote that you 'can see the interior only with your imagination'.
Augmented Rhombicuboctahedron | matematicas visuales
Starting with a Rhombicubotahedron we can add pyramids over each face. The we get a beautiful polyhedron that it is like a star.

12th February 2018

Geometry: Pseudo Rhombicuboctahedron
Pseudo Rhombicuboctahedron | matematicas visuales
This polyhedron is also called Elongated Square Gyrobicupola. It is similar to the Rhombicuboctahedron but it is less symmetric.

29th January 2018

Geometry: Triangles
Pythagoras Theorem: Baravalle's demonstration | matematicas visuales
Dynamic demonstration of the Pythagorean Theorem by Hermann Baravalle.

8th January 2018

Geometry: Triangles
Pythagoras Theorem: Euclid's demonstration | matematicas visuales
Demonstration of Pythagoras Theorem inspired in Euclid.

11th December 2017

Geometry: The World
Axial projection from the Sphere to the cylinder | matematicas visuales
This perpective projection is area-preserving. If we know the surface area of a sphere we can deduce the volume of a sphere, as Archimedes did.

27th November 2017

Geometry: The World
The World | matematicas visuales
Basic world map in a sphere. Latitude and longitude

19th November 2017

Geometry: Campanus' sphere
Campanus' sphere and other polyhedra inscribed in a sphere | matematicas visuales
We study a kind of polyhedra inscribed in a sphere, in particular the Campanus' sphere that was very popular during the Renaissance.

13th November 2017

History: Leonardo da Vinci
Leonardo da Vinci:Drawing of a SEPTUAGINTA 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 Campanus' sphere.

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