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Copyright © 2005 Pearson Education, Inc. Slide 10-1
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Copyright © 2005 Pearson Education, Inc. Slide 10-1
Copyright © 2005 Pearson Education, Inc.
Chapter 10
Copyright © 2005 Pearson Education, Inc. Slide 10-3
Points, Lines and Planes
A geometric point is imagined to have zero size. A geometric line is formed by connecting two
points along the shortest possible path. Line segments are pieces of a line A geometric plane is a perfectly flat surface that
has infinite length and width but no thickness.
10-A
point lineplane
Copyright © 2005 Pearson Education, Inc. Slide 10-4
Angles
The intersection of two lines or line segments
forms an angle.
The point of intersection is called the vertex.
10-A
Copyright © 2005 Pearson Education, Inc. Slide 10-5
Types of Angles
Right: measures 90 Straight: measures 180
Acute: measures less than 90 Obtuse: measures between
90 and 180
10-A
Copyright © 2005 Pearson Education, Inc. Slide 10-6
Polygons
10-A
Copyright © 2005 Pearson Education, Inc. Slide 10-7
Perimeter and Area
10-A
Copyright © 2005 Pearson Education, Inc. Slide 10-8
Surface Area and Volume
10-A
Copyright © 2005 Pearson Education, Inc. Slide 10-9
Platonic Solids
10-A
Copyright © 2005 Pearson Education, Inc. Slide 10-10
Scaling Laws
Lengths always scale with the scale factor.
Areas always scale with the square of the scale factor.
Volumes always scale with the cube of the scale factor.
10-A
Copyright © 2005 Pearson Education, Inc. Slide 10-11
Pythagorean Theorem
The Pythagorean theorem applies only to right
triangle (those with one 90 angle). For a right
triangle with side lengths a, b, and c, in which
c is the longest side (or hypotenuse), the
Pythagorean theorem states that
a2 + b2 = c2
10-B
a
b
c
Copyright © 2005 Pearson Education, Inc. Slide 10-12
Similar Triangles
10-B
Copyright © 2005 Pearson Education, Inc. Slide 10-13
Snowflake Curve & Fractal Dimension
10-C
The fractal dimension of an object is defined as a number D such that
N = RD
where N is the factor by which the number of elements increases when we shorten the ruler by a reduction factor R.
Copyright © 2005 Pearson Education, Inc. Slide 10-14
Sierpinksi Triangle Iterations
10-C
Copyright © 2005 Pearson Education, Inc. Slide 10-15
Sierpinksi Triangle Iterations
10-C
Copyright © 2005 Pearson Education, Inc. Slide 10-16
Sierpinksi Triangle Iterations
10-C
Copyright © 2005 Pearson Education, Inc. Slide 10-17
Sierpinksi Triangle Iterations
10-C
Copyright © 2005 Pearson Education, Inc. Slide 10-18
The Mandelbrot Set
10-C
Copyright © 2005 Pearson Education, Inc. Slide 10-19
Two Views of Barnsley’s Fern
10-C
Copyright © 2005 Pearson Education, Inc. Slide 10-20
A Fractal Landscape by Anne Burns
10-C
