Pizza Pie, Unrolled
2
The next slide is a graphic visualization of the fact that Pi (π) is always 3.14159… diameters, of any given circle, which is why the circumference, of any circle, equals πr2 (where r is the radius of the given circle). The cycloid curve—traced by a fixed point on a circle rolling smoothly in a straight line (e.g., a railway wagon wheel)—is close to but not quite circular: it forms an elliptic segment. While the circle is rolled at a fixed speed, the cycloid tracing point moves at varying speeds: at rest, accelerating to the top of the arch, then decelerating back to rest, and so on. Cycloid length = 8r (4× the defining circle’s diameter (not pi dependent!)), area = 3πr 2 (3× the defining circle’s area).
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Transcript of Pizza Pie, Unrolled
The next slide is a graphic visualization of the fact that Pi (π) is always 3.14159… diameters, of any given circle, which is why the circumference, of any circle, equals πr2 (where r is the radius of the given circle).
The cycloid curve—traced by a fixed point on a circle rolling smoothly in a straight line (e.g., a railway wagon wheel)—is close to but not quite circular: it forms an elliptic segment.
While the circle is rolled at a fixed speed, the cycloid tracing point moves at varying speeds: at rest, accelerating to the top of the arch, then decelerating back to rest, and so on.
Cycloid length = 8r (4× the defining circle’s diameter (not pi dependent!)), area = 3πr2
(3× the defining circle’s area).
Travelled distance = π = 3.14… circle diameters
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πZZAπ (Pizza Pie, Eight Radial Slices!)
Visualizing the circumference (of any circle)as 3.14159… circle diameters (radius r × 2).
Cycloid length = 8r, area = 3πr2
Press “Page Up” to reset the animation, thenPress “Page Down” to replay the animation
Copyright © 2010, Henry Norman
RelativePoint Speed
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Travelled distance = 8 radii (4 circle diameters)
