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Head First 2D Geometry by Dawn Griffiths, Stray

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the pythagorean theorem
Using Kwik-klik skate ramps is definitely the right angle!
By finding right triangles with whole number ratios between
the lengths of the sides, you’ve managed to build a whole load
of different ramps from the Kwik-klik standard parts. It’s a fast,
cheap, and smart way to build a skate course, and you’re in a
great position to reap the rewards.
That was so easy! I can’t
wait for the next one. Do
you want your cut of the
money now, or should I just
let it pile up for a while?
Unbelievable! Not only did the
course get assembled in a day but
man, it was the hottest street course
we’ve seen in a long time. Some
serious kick-flipping action was had
over some huge jumps, and we just
about tail-slid our way to heaven on
the excellent ramp-and-rail section.
Fran ‘five-oh’ Sampson took the
overall number one spot at the end
of the day, but we were all grinning
like winners thanks to Sam & Co’s
fantastic design-and-build efforts.
> click for pics
you are here 4 137
no dumb questions
To find the longest side, square the other two sides, add those up, and then find the
square root.
To find a short side, square the other two sides and subtract one from the other. Make
it a positive number and then find the square root.
Finding missing sides using the Pythagorean Theorem only works for right triangles.
Q:
But WHY? How come it adds up
like that?
A:That is a very good question and one
which mathematicians and philosophers
have struggled with for centuries.
Unfortunately there’s not always good “why”
reasons in geometry—stuff just IS. The
good news is that it’s very reliable…so
while understanding why the Pythagorean
Theorem works is beyond most of us, at
least we can make good use of it.
Q:
Why is it called The Pythagorean
Theorem? Why not something more
meaningful and easier to spell like
“Right triangle check” theorem?
A:Pythagoras was a Greek guy. He was
first to write down the theorem. That isn’t to
say that nobody had noticed it before, but
he gets the props. Shame he wasn’t called
something easier to spell!
Q:
I tried to use the Pythagorean
Theorem to find a missing short side,
and I was stuck trying to find the square
root of a negative number. What should
I do?
A:You’ve probably got your legs and
your hypotenuse mixed up. Try to redo
your subtraction the other way round. This
should give you a positive number, and
you’ll be able to find the square root.
Q:
So is “c” always the hypotenuse?
A:The Pythagorean Theorem uses “c”
for the hypotenuse and “a” and “b” for the
legs. Of course we know that algebra is just
a tool for describing a pattern, and in this
case, the pattern is what’s important: the
Q:
Do all triangles have a
hypotenuse? What if I have two long
sides of equal length and one short
side? Which is the hypotenuse?
A:Only right triangles officially have a
hypotenuse. And if you’ve got two sides
equally long, and one shorter one, your
triangle can’t have a right angle, because it
would fail the c
2
= a
2
+ b
2
test, whichever of
your longer sides you decided was “c”.
But don’t think you can’t use the
Pythagorean Theorem for triangles that
don’t have a right angle…it’s just takes a
little more thought to apply it. (More on that
in a minute.)
longest side squared equals the other
two sides squared. So, if you get mixed
up about your a, b, and c, think about what
the pattern behind that formula is, and go
from there.
OMG! Come read this
email—this is so cool…
you won’t believe it!
138 Chapter 3

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