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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matematicasVisuales has a page in Facebook. If you likes this site, go into and share matematicasVisuales.
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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.
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The Math Forum @ Drexel maintains an Internet Mathematics Library and they have chosen MatematicasVisuales as
Hot Spot for the month of August, 2010.
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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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This site matematicasVisuales has been linked as
an online resource in The Electronic Journal of Mathematics and Technology.
(September, 2012)
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6th May 2013
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The diagonal of a regular pentagon are in golden ratio to its sides and the point of intersection of two diagonals of a regular pentagon are said to divide each other in the golden ratio or 'in extreme and mean ratio'.
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1st April 2013
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The Second Fundamental Theorem of Calculus is a powerful tool for evaluating definite integral (if we know an antiderivative of the function).
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4th March 2013
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The Fundamental Theorem of Calculus tell us that every continuous function has an antiderivative and shows how to construct one using the integral.
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18th February 2013
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Power with natural exponents are simple and important functions. Their inverse functions are power with rational exponents (a radical or a nth root)
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3th February 2013
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The integral of power functions was know by Cavalieri from n=1 to n=9. Fermat was able to solve this problem using geometric progressions.
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3th January 2013
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Monotonic functions in a closed interval are integrable. In these cases we can bound the error we make when approximating the integral using rectangles.
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3th December 2012
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If we consider the lower limit of integration a as fixed and if we can calculate the integral for different values of the upper limit of integration b then we can define a new function: an indefinite integral of f.
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12th November 2012
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The integral concept is associated to the concept of area. We began considering the area limited by the graph of a function and the x-axis between two vertical lines.
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22th October 2012
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If the derivative of F(x) is f(x), then we say that an indefinite integral of f(x) with respect to x is F(x). We also say that F is an antiderivative or a primitive function of f.
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1st October 2012
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We can consider the polynomial function that passes through a series of points of the plane. This is an interpolation problem that is solved here using the Lagrange interpolating polynomial.
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17th September 2012
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We can see some basic concepts about integration applied to a general polynomial function. Integral functions of polynomial functions are polynomial functions with one degree more than the original function.
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27th August 2012
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To calculate the area under a parabola is more difficult than to calculate the area under a linear function. We show how to approximate this area using rectangles and that the integral function of a polynomial of degree 2 is a polynomial of degree 3.
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6th August 2012
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It is easy to calculate the area under a straight line. This is the first example of integration that allows us to understand the idea and to introduce several basic concepts: integral as area, limits of integration, positive and negative areas.
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