November 2009
Beginner
368 pages
8h 55m
English
Content preview from Head First 2D Geometry
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a pattern worth investigating
126 Chapter 3
The lengths of the sides are linked by a pattern
Did you find it? For the four right triangles we tested, it seems like the square of
the length of the longest side is equal to the squares of the other two sides added
together.
Triangle 3-4-5 6-8-10 5-12-13 9-12-15
Shortest-side’s
length
Middle-side’s
length
Longest-side’s
length
Shortest-side
squared
Middle-side
squared
Longest-side
squared
Shortest-side
squared +
middle-side
squared
3
4
5
9
16
25
9 + 16
= 25
6
8
10
36
64
100
36 + 64
= 100
5
12
13
25
144
169
25 +
144
= 169
9
12
15
81
144
225
81 +
144
= 225
This row
+
this row
= this row!
Right. So—for these four right triangles,
you get this freaky pattern. Don’t you think
if you’re gonna use this to design skate jumps
you need something a bit more reliable? What if
these are the ONLY four triangles it works for?
It doesn’t even make sense. What have squares
got to do with triangles anyway?
True. Can we really trust this pattern?
The numbers we’ve tested so far seem pretty conclusive,
but do we definitely know that this pattern is going to work
for all the possible right-angled jumps we might need?
And how do the squares relate to the triangles? Let’s
investigate this pattern in a more general way.
you are here 4 127
the pythagorean theorem
Geometry Investigation Magnets
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