Title: Geometry Applications: Geometry Basics: 3D Geometry

Title: Geometry Applications: Geometry Basics: 3D Geometry

[Music]

[Music]

IN ANCIENT GREECE THE PHILOSOPHER PLATO

DESCRIBED A SET OF THREE DIMENSIONAL SHAPES

THAT HAVE SINCE COME TO BEAR HIS NAME:

THE PLATONIC SOLIDS.

LET'S START WITH THEIR TWO DIMENSIONAL COUNTERPARTS

AND BUILD THEIR THREE DIMENSIONAL VERSION.

LOOK AT THIS EQUILATERAL TRIANGLE.

IT IS A REGULAR POLYGON

WHERE ALL SIDES AND ANGLE MEASURES ARE CONGRUENT.

THIS TWO DIMENSIONAL NET WHEN FOLDED THIS WAY

BECOMES THE THREE DIMENSIONAL SOLID

CALLED A TETRAHEDRON,

WHICH IS ONE OF THE PLATONIC SOLIDS.

BECAUSE OF THE UNDERLYING REGULAR POLYGON,

THE TETRAHEDRON HAS CONGRUENT EDGES,

VERTICES AND ANGLES.

NOW LOOK AT THIS SQUARE,

WHICH IS A REGULAR QUADRILATERAL.

WE USE THAT SQUARE TO CONSTRUCT

A TWO DIMENSIONAL NET.

WE FOLD THIS NET TO CONSTRUCT A CUBE,

WHICH IS ANOTHER PLATONIC SOLID

ALSO REFERRED TO AS A HEXAHEDRON.

THE "HEX" IN HEXAHEDRON REFERS TO SIX,

WHICH IS THE NUMBER OF SIDES IN A CUBE.

LIKE THE TETRAHEDRON

THE EDGES, VERTICES AND ANGLES OF THE CUBE

ARE CONGRUENT TO EACH OTHER.

THE OTHER PLATONIC SOLIDS INCLUDE THE

EIGHT-FACED OCTAHEDRON...

THE TWELVE-FACED DODECAHEDRON...

AND THE TWENTY-FACED ICOSAHEDRON.

WITH ALL THESE FIGURES,

THE UNDERLYING REGULAR POLYGON SHAPE

ENSURES CONGRUENT EDGES, ANGLES AND VERTICES.

BEYOND THE PLATONIC SOLIDS

ARE MANY DIFFERENT THREE DIMENSIONAL SHAPES.

IN THIS PROGRAM YOU WILL EXPLORE THE PROPERTIES

OF THREE DIMENSIONAL FIGURES.

UNDERSTANDING THE PROPERTIES OF THESE FIGURES

HELPS US UNDERSTAND CERTAIN NATURAL AND

MAN-MADE STRUCTURES THAT SHARE THESE PROPERTIES.

IN PARTICULAR, THIS PROGRAM WILL COVER

THE FOLLOWING KEY CONCEPTS: