Why does it not just get bigger and bigger and never end? I know that pi is the circumference of a circle.
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I think your a little confused.
Pi is not the circumference of a circle, it is the ratio of the circumference to the diameter of a perfect circle. And in relation to pi ending, it is not insurmountably large. The decimal places never repeat at any point, since it is an irrational number. Pi has no influence whatsoever on the size or properties of a circle.
Hope I clarified that well enough for ya!
Pi is not the circumference of a circle, it is the ratio of the circumference to the diameter of a perfect circle. And in relation to pi ending, it is not insurmountably large. The decimal places never repeat at any point, since it is an irrational number. Pi has no influence whatsoever on the size or properties of a circle.
Hope I clarified that well enough for ya!
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pi is not the circumference.
pi is a ratio
and on a perfect plane surface, it matches the ratio of the circumference to the diameter.
On a surface with positive curvature, the ratio of the circumference to the diameter could be less than pi.
For example, imagine Earth were a perfect sphere. You go to the North Pole and measure off a radius of 1800 nautical miles. Trace out the circumference (the circle will match the latitude of 60 N).
The circumference of this circle is 10,800 nautical miles.
Ratio = circumference/diameter = 10,800 / 3,600 = 3.000...
It gets better: keep increasing the length of the radius. When it reaches 10,800 nautical miles, the circumference will be... zero.
pi is a ratio
and on a perfect plane surface, it matches the ratio of the circumference to the diameter.
On a surface with positive curvature, the ratio of the circumference to the diameter could be less than pi.
For example, imagine Earth were a perfect sphere. You go to the North Pole and measure off a radius of 1800 nautical miles. Trace out the circumference (the circle will match the latitude of 60 N).
The circumference of this circle is 10,800 nautical miles.
Ratio = circumference/diameter = 10,800 / 3,600 = 3.000...
It gets better: keep increasing the length of the radius. When it reaches 10,800 nautical miles, the circumference will be... zero.
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Good question. The answer is that pi's decimal expansion never ends, but it does not become bigger. In fact, it's impossible for decimal expansions to make number grow bigger and bigger; they always hone in on a specific value.
Let's take pi for example. The first decimal approximation (without rounding) is 3. This means that pi is at least as big as 3, but could be as large as 4 (i.e. 3.99999...). The next approximation is 3.1. This means that it is definitely as big as 3.1, but could be as large as 3.2 (i.e. 3.1999...). Again, the next is 3.14, meaning that pi lies between 3.14 and 3.15. The band that pi could be in narrows (by a factor of 1/10) with each successive approximation. The infinite expansion merely points to exactly where pi lies on the number line, not makes it grow without bound.
Hope that helps!
Let's take pi for example. The first decimal approximation (without rounding) is 3. This means that pi is at least as big as 3, but could be as large as 4 (i.e. 3.99999...). The next approximation is 3.1. This means that it is definitely as big as 3.1, but could be as large as 3.2 (i.e. 3.1999...). Again, the next is 3.14, meaning that pi lies between 3.14 and 3.15. The band that pi could be in narrows (by a factor of 1/10) with each successive approximation. The infinite expansion merely points to exactly where pi lies on the number line, not makes it grow without bound.
Hope that helps!
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Because pi does end actually and a perfect circle ends too