Wikiversity:Stream/Circle
Circle - Introduction
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History:
In ancient times the circle, due to its perfect symmetrical properties, was believed to be divine.
So not only was it symbol for the sun, but all the planets had to move around the Earth in circular movements as well.
As this did not match observations, tricky adaptations of combined circular movements were constructed. It was Kepler who proposed the concept of elliptic planet movements.
Qualitative description:
A circle is a FLAT, ROUND FORM, it has NO BEGINNING and NO END, it has a CENTER, it looks very SYMMETRICAL.
Additionally a circle is relatively ABSTRACT, we do not find perfect circles in nature, but close approximations.
Examples:
The full moon appears as a really nice circle.
If we cut a pineapple in the middle, its center looks like a circle.
Crop circles (believed by some to be produced by Aliens) are sometimes very good circular approximations.
Construction:
Hold a small tree, stretch your arm, and walk around the tree. When you reach the starting point again, you have just constructed a circle.
We have found the basic property of circles here: At any position on the circle, our distance to the centre point (in our case: the tree) is the same.
Other constructional possibilities are a horizontal cut of a cone or the straight projection of a sphere.
Mathematical definition:
In the mathematical language we formulate our observations like this: A circle is a two-dimensional geometrical form, whose points all have a constant distance from a common center point.
Technical Application:
There are two very important technical aspects:
- Circles provide the largest area in relation to their periphery
- Forms with circular cross section (e.g. cylinders) provide the best possible stability against certain forces (pressure and torque)
Similar Forms:
- Ellipse: A circle can also be regarded as a special form of ellipse with coincidental focal points.
- Sphere: A sphere can be regarded as a three dimensional (rotating) circle.
- Straight line: Contradictory as it may sound, a straight line can be regarded as a circle with infinite radius. Very strange property of this straight circle – it has an infinite number of central points in infinity.
Other Languages:
Exercise:
Try to draw a couple of circles free-handed. Calligraphers have perfected this technique and draw extremely exact circles.
See also:
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Remark: As you may note there is not a single formula in this article - consciously: We first have to transport concepts and make them comprehensible before we can start introducing formalistic languages. A linguistic mathematical description is given (s. above), but abstract formulas are avoided to reduce fear of contact. Math is by far not the only way to scientifically look at phenomena, as was shown here. Besides, there should be the greatest possible variety of directions to develop knowledge by a network of links for each aspect. |