# geogebra

An epicycloid with one cusp rolling inside an epicycloid with two cusps rolling inside an epicycloid with three cusps rolling inside…

Dudeney dissection from a square to an equilateral triangle. Only 4 pieces!

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In the left, the original Jansen’s mechanism with it’s walking curve, and in the right, a simplified version.

A la izquierda, el mecanismo original de Jansen y su “curva de caminata”, y a la derecha una versión simplificada.

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Parametric curves

This is showing all the parabolas with the same focus that go through the same point.

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.

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## Spin Planes

Inspired by the Regolo54 piece at the top. Always amazing hand-drawn #mathart.

I started messing around with dynamicized symmetry and design. Got the spinning dilations looking okay, but not the intersecting. Gan’t get the spiral piece on the ones that look like they’re intersecting. Fun to play, though.

Both are on GeoGebraTube: spinning, intersecting

Area of a circle

Interactive version:

x = t cos(t)

y = t sin(t)

x = (−1) t cos(t)

y = (−1) t sin(t)

x = t sin(t)

y = (−1) t cos(t)

x = (−1) t sin(t)

y = t cos(t)

0 ≤ t ≤ 5.5 π

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Parametric curves by[R-D]

La mia arte matematica. Queste figure ricordano vecchi merletti, solo che sono ottenute attraverso  equazioni.

Enjoy!

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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

I made it a little more complicated xD #geometry #math #computer #geogebra (Taken with Instagram)

Rolling hypocycloids

Interactive GeoGebra-version:

Made with GeoGebra. You need a slider for your animation be exported as GIF, took me a couple of hours to figure it out :P

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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

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Parametric curves by[R-D]

Brownie Math

Nice post by Geoff about a number of investigations from an interesting brownie pan. He asked about a GeoGebra sketch and I couldn’t resist.

GeoGebra file at the Tube.