Idiot\'s Guides Basic Math and Pre-Algebra

210 Part 3: The Shape of the World

A circle is defined as the set of all points at a
fixed distance from a given point. Let’s keep
things simple in the beginning and use the origin
as the center point. That will mean that the circle
is all the points that are r units from the point
(0,0) for whatever radius r you pick. Let’s have
r = 5 for our example.

Finding the first few points is easy. From the
origin, count 5 up and put a point at (0,5). Then
count 5 down from the origin and put a point at
(0,-5). Do a left and right move and put points at
(5,0) and (-5,0). With those points you can imagine
what the circle might look like, but it would be
easier to draw it with a few more points.

Do you remember the distance formula? It’s the
one that says the distance between two points
xy 11 , and xy 22 , is dxx yy 21 ^2  212.
And do you remember that the distance formula
is just the Pythagorean Theorem in disguise?

You know that every point on the circle is 5 units
away from the origin, so if you put a 3-4-5 right
triangle with one vertex at the origin and one leg

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along the x-axis, the other end of its hypotenuse

will be 5 units from the origin.

You can use that 3-4-5 right triangle like a mea-

suring stick, putting it in different positions, and

you get more points on your circle. When it looks

like this, it will be easy to connect the dots.

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