geogebra

Al construir cuadrados sobre los lados de un triángulo cualquiera, se determinan otros triángulos con la misma área del inicial. Esta animación ilustra tal idea, de manera que el triángulo se transforma manteniendo su área.


When constructing squares over the sides of any triangle, other triangles are determined, with the same area as the initial one. This animation demonstrates such idea, given that the transforming triangle maintains its area.

(vía Geometría Dinámica » El lenguaje de la geometría)

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Sangaku Synchronicity.

I love the Japanese sacred geometry known as sangaku. As I was preparing for a class on proof in HS geometry, I was thinking about what could add a level of intrigue to the circle, triangle and parallel line proofs - and thought of sangaku. I became quite taken with the 5 circles in a square one pictured above; beautiful Pythagorean Theorem connections.

I was pretty stumped working it out, so I set it up in GeoGebra to trace the possible squares - and found that gorgeous limaçon hiding! Wow!

So then I had to work up the whole thing in GeoGebra. Serendipity in math is a sweet thing, no?

If you’d like more, Jean-Paul Berroir has some gorgeous Sangaku on GeoGebraTube

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One side of a triangle slides over the coordinate axes, so the third vertex describes an ellipse. Depending of the characteristics of the triangle, ellipses of different sizes and orientation are described, including the cases of degenerates triangles of zero height, which generate ellipses with vertices over the coordinate axes; and the case of an ellipse degenerated into a segment, when the triangle is a right isosceles one.

Los lados de un triángulo se deslizan sobre los ejes coordenados, de manera que su tercer vértice describe una elipse. Dependiendo de las características del triángulo se generan elipses de distintas dimensiones y orientación, incluyendo los casos degenerados de un triángulo con altura 0, que genera una elipse con vértices sobre los ejes coordenados; y el caso de la elipse que se degenera en un segmento cuando el triángulo es isósceles rectángulo.

Idea basada en el applet “Generación de una elipse” de la exhibición Imaginary (y recomendada por ^DiAmOnD^, de Gaussianos.com).

Este post participa en la Edición 3.14159 del carnaval de matemáticas en español, cuyo anfitrión es el blog Scientia