The Platonic Solids

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Slide with some basic explanations

Technology Education

Index of Contents ,[object Object],[object Object],[object Object]

1. A brief review of some geometry concepts ,[object Object],[object Object],[object Object],[object Object]

2. The platonic solids and their magic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

2. The platonic solids and their magic ,[object Object],[object Object],[object Object],[object Object]

3. A taste of their history ,[object Object],[object Object],[object Object]

3. A taste of their history ,[object Object],[object Object]

3. A taste of their history ,[object Object]

Epilogue ,[object Object],[object Object]

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Greeks Bearing Gifts A great concern among Greek philosophers, most notably Plato and Aristotle, was the meaning of universals, or forms. When a person uses the word dog, to what do they refer? In the famous quote, “Outside of a dog, a book is man’s best friend. Inside of a dog, it’s too dark to read…” the form or universal dog is being discussed. Some dogs are tall, others short. They occur in a variety of colors. Some are friendlier than others. Yet they all share something or they wouldn’t be dogs. The Greek philosophers were interested in the abiding essence of dog.1 After all, every dog on this planet will eventually die – but “dogness” will go on forever, we hope. This is called the problem of universals in philosophy and it has many different answers. The famous fourth-century (B.C.) philosopher Plato believed that there is a perfect dog which resides in the world of universals – a mystical place where our immortal souls come from prior to our birth. This universal dog is stripped of all of its nondog-specific characteristics. It has no specific color or height or weight. It wouldn’t be your pet, Fango, because he is a specific dog, while the universal dog has only general characteristics essential to every dog. Plato’s perfect puppy will never die – and it doesn’t have to be walked. It is truly the ideal dog. In fact, the term “ideal” comes from Plato’s world. The forms there give us the “idea” of dog, cat, man, or whatever class of things we have the idea of. The forms are eternal and worthy of our study, whereas earthly objects are imperfect shadows of the forms. You may have read Plato’s cave analogy in his book The Republic, in which he expounds on this theme. It should come as no surprise that Plato loved geometry. Geometry establishes necessary connections between the forms of the polygons we see around us. We don’t speak of this rectangular table or that circular clock on the wall in geometry. We discover truths, rather, of the perfect circle or the perfect rectangle. These are eternal truths. Plato founded a school of philosophy which he named the Academy, and legend has it that he wrote over its portals “Let none enter here who have not studied geometry.” Geometric truths, thought Plato, are apprehended through pure reason, unsullied by perception. The diagrams simply allow us to recollect things our souls knew in that other world (of universals). A legacy of his is “Platonic Love” – pure and chaste – a love of the eternal soul of the other person unblemished by carnal (and temporary) lust for the flesh. You can imagine that Plato wasn’t the life of the party. Aristotle, a student of Plato’s, departed from all of this. He rejected the world of universals, maintaining that the essence of dog resides in each dog. Perception, without reason, however, will not reveal the essence. Rather, we form the idea of dog by inducing it from observation of many particular dogs. Their differences aside, these great philosophers, including Pl ...

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