Calculating Vertices & Edges on a Cube - Geometry for Beginners

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SUMMARY

The discussion focuses on calculating the number of vertices and edges of a cube using mathematical principles rather than simple counting. A cube has 8 vertices and 12 edges, with each face sharing 4 edges. The participants reference Euler's formula, F + V - E = 2, where F represents the number of faces, V the number of vertices, and E the number of edges, allowing for the calculation of one variable when the others are known. The conversation also touches on the need for beginner-friendly geometry resources.

PREREQUISITES
  • Understanding of basic geometric concepts such as vertices, edges, and faces.
  • Familiarity with Euler's formula in geometry.
  • Basic mathematical skills for solving equations.
  • Knowledge of cube properties and structure.
NEXT STEPS
  • Study Euler's formula in detail and its applications in polyhedra.
  • Explore the properties of different geometric shapes, focusing on polyhedra.
  • Read "Geometry for Beginners" by G. A. Hill for foundational concepts.
  • Investigate other beginner-friendly geometry textbooks or resources.
USEFUL FOR

Students new to geometry, educators seeking teaching resources, and anyone interested in understanding the mathematical properties of geometric shapes.

Bashyboy
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Hi, I was wondering how to calculate, mathematically, the number of vertices on a cube, rather than just count them? Also, in a cube, how many edges are shared by a face? By counting the number of edges, there comes out to be 24, but since it face shares four edges, shouldn't there be 6 edges then? I am trying to calculate both of these without counting. I am reading geometry for beginners by G. A. Hill, written in 1884; it is profoundly interesting, but since I never took geometry, I just don't have an intuition for it. Is there perhaps a simpler book that someone could suggest, for now to read?
 
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Ah yes, I remembering learning about this a long time ago, you have a formula along the lines of F+V-E=2. This is Euler's formula, where F= the number of faces, V= the number of vertices, and E=the number of edges. So you can solve for the third one by knowing the other two.
 

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