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The Fractal Logic of ARTriangles

ARTriangles products are probably the most sophisticated mosaic tiling systems ever offered. In order to become familiar with the fractal symmetry embodied in these shapes, it is useful to perform a few basic manipulations. Based on the Golden or Divine Proportion, the acute triangle consists of two long sides and one short. The obtuse triangle has two short sides and one long. For the first exercise, arrange ten acute triangles into a circle. Next arrange ten obtuse triangles into a star made of five mirrored tiles. An infinite number of mosaic designs can be created with various pieces of these stars and circles. Start simple and see what each of these triangles can do. You can make stars

Teaching Self-Discovery

Anyone would agree that figuring something out on your own is satisfying, and often preferable to being told what to do. Some concepts such as proportion are difficult to teach. That is where ARTriangles provide a creative environment for discovering geometric proportion with no instruction necessary. Arranging these triangles into inventive designs helps you discover their self-organizing nature and begin to glimpse their unique properties. ARTriangles' limitless designs challenge the imagination. Anyone can come up with something original and creative, whether simple or complex. Group activities bring shared delight and discovery. For example, each student can take turns placing triangles

History of the Golden Proportion

In the 6th century B.C., the Greek philosopher Pythagoras, best known for the Pythagorean Theorem, adapted the pentagram as a symbol representing health. Its proportions were derived from what is now known as the Golden Proportion. Pythagoras' world views were highly influenced by mathematics and mysticism. During the European Renaissance, the Golden Proportion was revisited by the Italian mathematician Luca Pacioli, known as the father of accounting. Luca Pacioli taught in many universities in his lifetime and was a prolific writer. One of his textbooks, printed in Venice in 1494, was Summa de Artihmetica, Geometrica, proportioni et propotionalitá (Everything about Arithmetic, Geometry and

ARTriangles Site Reviews

Early reviews as ARTriangles ramps up

“I get more excited each time I look at your website (three times now).”
--Selina

“Website looks awesome. Especially loved the woodtone mandalas.”
--Alma

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