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Students Class Work – The Wheel of Theodorus


“A mathematician, like a painter or poet, is a maker of patterns”  G.H. Hardy

This month, as part of the Differential Calculus class in 11th Grade, the students in Guillermo Marín’s group have been learning about The Wheel of Theodorus, a spiral composed by right triangles, used to prove that square roots of non-square integers from 3 to 17 are irrational

The Wheel allows students to discover patterns through the construction of such right triangles. The spiral starts with an isosceles right triangle, with legs of 1 unit length; then, the Pythagorean Theorem is used to find the value of the hypotenuse. Afterwards, a new right triangle is made using as one of the legs the hypotenuse of the prior triangle, and the other leg, a new segment of 1 unit length. Then, after all triangles have been built, a beautiful spiral is formed.

Students were asked to creatively turn the wheel into something colorful and make some art work to resemble that math is everywhere in our lives. We celebrate learning and congratulate both, Guillermo and his students, for this display of creativity and learning! Enjoy!

Art creations by:

Valentina Pérez Daniela Borda Paula Buitrago Stephany Strauch Juliana Uribe


Resumen: en la clase de Cálculo Diferencial en 10º, los estudiantes del grupo del profesor Guillermo Marín, han estado aprendiendo sobre la “Rueda de Theodorus”. Ésta es una espiral compuesta por triángulos rectángulos, y se usa para probar que las raíces cuadradas de los números enteros no cuadrados, del 3 al 17, son irracionales. 

Los resultados de sus trabajos son ¡espectaculares! Así pues, los estudiantes transformaron de manera creativa sus espirales en algo colorido y en obras de arte para mostrar que las matemáticas están en todas partes. ¡Celebramos el aprendizaje y felicitamos a Guillermo y sus estudiantes por su creatividad y aprendizaje! 

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