Pitagoras
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![Pythagoras' Theorem in a tiling | matematicasVisuales Pythagoras' Theorem in a tiling | matematicasVisuales](../../../images/appimg/pythagoras.jpg) |
We can see Pythagoras' Theorem in a tiling. It is a graphic demonstration of Pythagoras' Theorem we can see in some floor made using squares of two different sizes.
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Archimedes
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![Archimedes' Method to calculate the area of a parabolic segment | matematicasVisuales Archimedes' Method to calculate the area of a parabolic segment | matematicasVisuales](../../../images/appimg/archimedesparabola.jpg) |
Archimedes show us in 'The Method' how to use the lever law to discover the area of a parabolic segment.
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![Archimedes and the area of an ellipse: an intuitive approach | matematicasVisuales Archimedes and the area of an ellipse: an intuitive approach | matematicasVisuales](../../../images/appimg/areaellipse.jpg) |
In his book 'On Conoids and Spheroids', Archimedes calculated the area of an ellipse. We can see an intuitive approach to Archimedes' ideas.
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![Archimedes and the area of an ellipse: Demonstration | matematicasVisuales Archimedes and the area of an ellipse: Demonstration | matematicasVisuales](../../../images/appimg/archimedesellipse.jpg) |
In his book 'On Conoids and Spheroids', Archimedes calculated the area of an ellipse. It si a good example of a rigorous proof using a double reductio ad absurdum.
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Leonardo da Vinci's drawings for Luca Pacioli's book 'De divina proportione'
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![Leonardo da Vinci: Drawing of a dodecahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales Leonardo da Vinci: Drawing of a dodecahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales](../../../images/appimg/leonardododecahedron.jpg) |
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the dodecahedron.
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![Leonardo da Vinci: Drawing of a truncated octahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales Leonardo da Vinci: Drawing of a truncated octahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales](../../../images/appimg/leonardotruncatedoctahedron.jpg) |
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 octahedron.
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![Leonardo da Vinci: Drawing of a cuboctahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales Leonardo da Vinci: Drawing of a cuboctahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales](../../../images/appimg/leonardocuboctahedron.jpg) |
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the cuboctahedron.
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![Leonardo da Vinci: Drawing of an stellated octahedron (stella octangula) made to Luca Pacioli's De divina proportione. | matematicasVisuales Leonardo da Vinci: Drawing of an stellated octahedron (stella octangula) made to Luca Pacioli's De divina proportione. | matematicasVisuales](../../../images/appimg/leonardostellatedoctahedron.jpg) |
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the stellated octahedron (stella octangula).
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![Leonardo da Vinci: Drawing of a truncated tetrahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales Leonardo da Vinci: Drawing of a truncated tetrahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales](../../../images/appimg/history/leonardotruncatedtetrahedron.jpg) |
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.
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![Leonardo da Vinci:Drawing of an octahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales Leonardo da Vinci:Drawing of an octahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales](../../../images/appimg/history/leonardoroctahedron.jpg) |
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the octahedron.
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![Leonardo da Vinci:Drawing of a rhombicuboctahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales Leonardo da Vinci:Drawing of a rhombicuboctahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales](../../../images/appimg/history/leonardorhombicuboctahedron.jpg) |
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the rhombicuboctahedron.
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![Leonardo da Vinci:Drawing of a SEPTUAGINTA made to Luca Pacioli's De divina proportione. | matematicasVisuales Leonardo da Vinci:Drawing of a SEPTUAGINTA made to Luca Pacioli's De divina proportione. | matematicasVisuales](../../../images/appimg/history/leonardoseptuaginta.jpg) |
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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![Leonardo da Vinci:Drawing of an augmented rhombicuboctahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales Leonardo da Vinci:Drawing of an augmented rhombicuboctahedron made to Luca Pacioli's De divina proportione. | matematicasVisuales](../../../images/appimg/history/leonardoaugmentedRCO.jpg) |
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.
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![Leonardo da Vinci:Drawing of an augmented rhombicuboctahedron made to Luca Pacioli's De divina proportione (2). | matematicasVisuales Leonardo da Vinci:Drawing of an augmented rhombicuboctahedron made to Luca Pacioli's De divina proportione (2). | matematicasVisuales](../../../images/appimg/history/leonardoaugmentedRCO2.jpg) |
We can see the interior of the augmented rhombicuboctahedron. Luca Pacioli wrote that you 'can see the interior only with your imagination'.
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Durer
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![Durer's approximation of a Regular Pentagon | matematicasVisuales Durer's approximation of a Regular Pentagon | matematicasVisuales](../../../images/appimg/history/durerpentagon.jpg) |
In his book 'Underweysung der Messung' Durer draw a non-regular pentagon with ruler and a fixed compass. It is a simple construction and a very good approximation of a regular pentagon.
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![Durer and transformations | matematicasVisuales Durer and transformations | matematicasVisuales](../../../images/appimg/durer.jpg) |
He studied transformations of images, for example, faces.
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![Albert Durer and ellipses: cone sections. | matematicasVisuales Albert Durer and ellipses: cone sections. | matematicasVisuales](../../../images/appimg/history/durerellipse.jpg) |
Durer was the first who published in german a method to draw ellipses as cone sections.
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![Albert Durer and ellipses: Symmetry of ellipses. | matematicasVisuales Albert Durer and ellipses: Symmetry of ellipses. | matematicasVisuales](../../../images/appimg/history/durerellipsesymmetry.jpg) |
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 .
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Kepler
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![Kepler: The Area of a Circle | matematicasVisuales Kepler: The Area of a Circle | matematicasVisuales](../../../images/appimg/keplercircle.gif) |
Kepler used an intuitive infinitesimal approach to calculate the area of a circle.
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![Kepler: The volume of a wine barrel | matematicasVisuales Kepler: The volume of a wine barrel | matematicasVisuales](../../../images/appimg/keplerbarrel.jpg) |
Kepler was one mathematician who contributed to the origin of integral calculus. He used infinitesimal techniques for calculating areas and volumes.
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![Kepler: The best proportions for a wine barrel | matematicasVisuales Kepler: The best proportions for a wine barrel | matematicasVisuales](../../../images/appimg/kepler.jpg) |
Studying the volume of a barrel, Kepler solved a problem about maxima in 1615.
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![Kepler: The volume of a wine barrel. Another look | matematicasVisuales Kepler: The volume of a wine barrel. Another look | matematicasVisuales](../../../images/appimg/history/keplerbarrel2.jpg) |
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.
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Cavalieri
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![Cavalieri: The volume of a sphere | matematicasVisuales Cavalieri: The volume of a sphere | matematicasVisuales](../../../images/appimg/cavalierisphere.jpg) |
Using Cavalieri's Principle we can calculate the volume of a sphere.
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The Logarithm Function
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![Mercator and Euler: Logarithm Function | matematicasVisuales Mercator and Euler: Logarithm Function | matematicasVisuales](../../../images/appimg/mercatoreuler.gif) |
Mercator published his famous series for the Logarithm Function in 1668. Euler discovered a practical series to calculate.
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