THE AREA OF A CIRCLE
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THE
LENGTH OF A CIRCUMFERENCE THE AREA OF A CIRCLE |
| Geometry | |
| 1. THE LENGTH OF A CIRCUMFERENCE | ||
| We can think of a circumference as being a polygon with a large number of sides. We have already seen how the edge of a many-sided polygon looks like a circumference in the Descartes programme. If we compare the perimeter of a regular polygon with the length of the circumference that circumscribes it we can see that the more sides the polygon has the closer its perimeter is in length to that of the circumference. | ||
1.-
Find
out how many sides a polygon has when its perimeter is the same length
as its circumcircle. Are they really exactly the same length or do
they just look the same length because of the number of decimal places
given in the window?
2.- If we don't know the value of p we can work it out approximately by finding the perimeter of a 1,000-sided polygon inscribed in the circle.
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| 2. The area of a circle | ||
| We have seen how the perimeter of a regular polygon and its circumcircle become more and more similar as the number sides of the polygon is increased. In the same way, the area of a polygon becomes closer in value to that of the circle as the number of sides becomes greater. | ||
| 3.- Increase
the number of sides until the values for the area of the polygon and
the circle become the same. |
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| Miguel García Reyes | ||
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| Spanish Ministry of Education. Year 2001 | ||
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