PPT-Platonic Solids

MATH 420 Presentation Kelly Burgess What are they Convex Polyhedron polyhedron 3d solid with straight edges and flat faces All faces are congruent Same number of faces meet at each vertex Named after Greek philosopher Plato who associated each with a basic element. & Platonic Solids Vertices/Nodes: The common endpoint of two or more rays or line segments. Edges: the line segments where two surfaces meet Faces/Regions: Interior: area containing all the edge Module 1. Session Topics. Surfaces and Solids of Revolution. Degree of Revolution. Hollow Objects. Visualizing Revolution. Surfaces and Solids of Revolution. Surfaces and Solids of Revolution are formed when a 2-D shape is revolved about an axis. J. Blackmon. Platonic Forms. Platonic Forms. The Problem. We encounter particular instances of justice, but how do we come to know justice?. We encounter particular triangles, but how do we come to know about . Sebald. Geometric Solids. Introduction. Geometric Solids are 3-Dimensional (or “3-D”) shapes – which means they have the 3 . dimensions. of width, depth, and height. Basic examples are spheres, cubes, cylinders, and pyramids. But there are lots of others. Some geometric solids have . Microscopic to Macroscopic. Macroscopic vs. Microscopic. Macroscopic means from the big picture or from far away.. This means what we can see with the naked eye.. Microscopic means from close up or on a small scale.. Jim Olsen. Western Illinois University. JR-Olsen@wiu.edu. Platonic ~ Archimedean. Plato. (423 BC –347 BC). Aristotle. (384 BC – 322 BC). Euclid. (325 and 265 BC). Archimedes . (. 287.  BC –. The Platonic Solids as Tiffany lamps, art objects, and stepping stones to higher dimensions. Carlo H. . Séquin. & Hans . Schepker. CS Professor,. U C . Berkeley. Artist,. Harrisville, NH. Basel, Switzerland. Solids. Crystalline Solids- have a regular repeating arrangement of their particles.. Salts, Sugars, Metals. Amorphous Solids- have no regular repeating arrangement of their molecules. Common glass, several polymers.. SCH4U1. Mr. . Dvorsky. Ionic Solids. Result from the reaction of a metal and a non-metal. Because of the large . electronegativity. difference, electrons transfer from the metallic atom to the non-metallic atom and the ions that result attract each other. . Grade 9 Math. Platonic solids. E4 Make and apply generalizations about the properties of platonic solids. To prepare for this lesson. What is a polygon? . What are some polygons you know?. What is a regular polygon?. FROM MANURE DIGESTATE. Biocycle. REFOR 17. Portland OR. October 18, 2017. Craig Frear, PhD. Director of Research and Technology. Regenis. Examples of Fine Solids Separation Technologies. Use of gravitational forces, chemical flocculation, filtration, and/or pressure to separate suspended solids from wastewater—while using a variety of dewatering methods to produce a stackable solid product. . All . faces, all edges, all corners, are the . same.. They are . composed . of . regular 2D polygons:. There were infinitely many 2D n-. gons. !. How many of these regular 3D solids are there?. Making a Corner for a Platonic . Investigating Regular Polyhedra– Level 1. What You’ll Learn…. What the Platonic solids are, what makes them unique, and how they relate to one another.. The math behind these special shapes and why there is a limited number of regular polyhedra. . Salts, Sugars, Metals. Amorphous Solids- have no regular repeating arrangement of their molecules. Common glass, several polymers.. Crystalline Structure. Amorphous. Amorphous solids. Amorphous solids, due to a lack of arrangement of molecules, .