PPT-The Platonic Solids

In Perspective Symmetry and Regularity Objects that are symmetrical look the same from several different views or two sides are mirror images of each other Symmetric solids are referred to as regular or Platonic solids. & 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 . th. Dimension – and beyond!. The Power and Beauty of Geometry. Carlo. . Heinrich. . Séquin. University of California, Berkeley. Basel, Switzerland. Math Institute, dating back to 15. th. century. -Describe . these objects-. What are some things that you notice?. Have you ever seen anything like these? Where?. What do they remind you of?. How would you describe these objects?. How can we describe these using geometric terms?. The molecular compounds like water, ammonia, and carbon dioxide have different physical properties because of the intermolecular forces.. Comparison of all three phases:. Liquids & Solids. Liquids & Solids. ● . Phases and Phase Diagrams. ● Liquids and Liquid Properties. ● Intermolecular Forces. ● Heating Curves. ● Introduction to Solids. ● Cubic Packing Arrangements. ● Closest-Packed Structures. 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 . 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.. Beaker. USE:. Holds solids or liquids. Poor accuracy- only estimates volume. Hot Hands. USE:. Use to hold beakers when warm. Should not be used when liquid is boiling. Graduated Cylinder. USE:. Measure volumes of liquids. Geometry. Chapter 12. This Slideshow was developed to accompany the textbook. Larson Geometry. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. 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 . 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, .