
Towards Pi 3.141552779 Hand Drawn

by Jason Padgett
Original - Sold
Price
$2,500
Dimensions
20.000 x 18.000 inches
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Title
Towards Pi 3.141552779 Hand Drawn
Artist
Jason Padgett
Medium
Drawing - Pencil On Paper
Description
This drawing represents the fascinating nature of Pi and its relationship to circles. As the number of sides in a polygon increases, approaching infinity, the value of Pi forever approaches the concept of a circle. This website showcases three variations of Pi by Jason Padgett with increasing numbers of sides, illustrating how the shape becomes smoother and closer to a circle with each iteration.
The inner and outer boundaries of Pi are explored through the use of secant and tangent lines. Secant lines approach Pi from the inside of the circle, while tangent lines approach Pi from the outside of the perimeter. As these lines converge, they encapsulate Pi within a forever-smoothing shape, forever closer to a circle. It's important to note that perfect circles don't exist in reality.
To visualize this concept, observe the three drawings of Pi side by side. The one with 180 sides shows significant empty spaces on the circle's edge. Moving to the drawing with 360 sides, some of that empty space is filled in, bringing it closer to a circle. Finally, the drawing with 720 sides fills in even more space, approaching the circular form. The beauty of Pi lies in the fact that it continually approaches a circle without ever reaching it, offering an infinite progression.
The precise equation for the area of this shape involves the number of sides (n) and the radius (r): 360sin(180/360)r^2 (in degree mode on a scientific calculator). Similarly, the circumference equation is 2(sin(180/360))r in degree mode or 2(sin(Pi/360))r in radians. As more sides are added, the area and circumference of Pi become increasingly unique and distinct. This is why Pi can never repeat itself mathematically, as the addition of sides perpetually generates new values.
The concept of infinity poses a challenge when measuring Pi, as it describes a shape perpetually approaching a circle. Attempts to measure a shape in motion are inherently limited. This problem resonates with the "Yardstick" or "Coastline" problem in fractal geometry, where using a smaller measurement tool yields a more accurate result but implies an infinitely large perimeter.
In the realm of physics, the application of the Planck length offers a way to circumvent this issue. The Planck length represents the smallest observable distance in our universe. By considering circles with sides equal to the Planck length, we approach the closest possible observation of a perfect circle within our physical limitations.
Uploaded
December 1st, 2011
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