Geometry for Elementary School/Points
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| Geometry for Elementary School | ||
| Our tools: Ruler and compass | Points | Lines |
A Point is the limit of a circle whose size is decreasing.
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The reason that this shape is not a point is that it is too large, it has area. This is a 'ball'. |
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Even when taking a ball of half that size we don't get a point. |
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And that is too large as well... |
We can consider that the "ball", circles, and the other non-points heve and represent points at their centers. A point can also be considered to exist where two lines cross, (Such as +, X, and * ).
A point is so small that even if we divide the size of these balls by 100, 1,000 or 1,000,000 it would still be much larger than a point. A point is considered as infinitely small. In order to get to the size of a point we should keep dividing the ball size by two - forever. Don't try it at home.
A point has no length, width, or depth. In fact, a point has no size at all. A point seems to be too small to be useful. Luckily, as we will see when discussing lines we have plenty of them. It may be best to think of a point as a location, as in a location where two lines cross.
Why define a point as an infinitely small dot? For one thing it has a very precise location, not just the center of a rough dot, but the point itself. Another reason is that if the drawing is made much bigger or smaller the point stays the same size. A point which is an infinitely small dot would be too small to see, so we must use a big old visible normal dot, or where two lines cross to represent it and its approximate location on paper.
