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# Locus and Definition of a Circle and Sphere - Concept

###### Brian McCall

###### Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

A locus is a set of points that meet a given condition. The definition of a **circle locus** of points a given distance from a given point in a 2-dimensional plane. The given distance is the radius and the given point is the center of the circle. In 3-dimensions (space), we would define a sphere as the set of points in space a given distance from a given point.

A term in Geometry that's a little bit confusing is Locus and we're not talking about one of the plagues here. we're talking about a set of points that meet a given condition, so to examine what this means let's look at 2 examples, first one says draw all the points 5 centimeters away from point p in the plane. So here's point p the plane would be the plane of the board. Remember planes are 2 dimensional and they extend infinitely in every direction. So if I start to think about well 5 centimeters you know just probably about right there and a point 5 centimeters away from point p could be right there. I can also have a point on the other side of point p and I can continue finding points that are about 5 centimeters away from point p until I'm blue in the face.

And as you're going to see eventually if I did this for long enough I would have a circle. So a locus is all of these points that meet a specific condition in which case this one said 5 centimeters away from point p in that plane. Which leads us to our definition of a circle, which is the locus of points at given distance away from a given point in a plane. So it's kind of a long way of saying if I give you a point a circle by definition is all those points that are certain distance away from that point that I gave you.

Let's go back to the second example, second example says draw all the points 5 centimeters away from point o in space. So we've got point o and obviously I won't be able to draw space which is coming out at you and it's going into the board but I can kind of make a guess. Well what it's going to look like is we're going to have all of these points o that'll be in the plane of the board and then we're going to have points that are going to come out of the board so I guess what I can do is I can draw a kind of a curve here which will show all the points that are coming up and I'm going to draw a dotted line for all the points that go into the board back into the board that are 5 centimeters away. So what we've drawn here is a sphere so that's the definition of a sphere which is related to a circle plus spheres talking about 3 dimensions. So it's the locus of points that are a given distance away from a point in space. So we're talking about 3 dimensions which is the space that we live in. So the key concept there is that a locus is all of the points that meet a given condition.

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###### Brian McCall

B.S. in Chemical Engineering, University of Wisconsin

J.D. University of Wisconsin Law School (magna cum laude)

He doesn't beat around the bush. His straightforward teaching style is effective and his subtle midwestern accent is engaging. There's never a dull moment with him.

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