Construct a spiral by starting at
the origin of a coordinate system,
moving 1 unit to the right to the
point (1, 0), then turning left 45
degrees and moving ½ unit, then
turning left 45 degrees and moving
⅓ unit, turning left 45 degrees and
moving ¼ unit, etc.
What are the
(x, y) coordinates of the limiting
point of this spiral?
You can get an closed form using Wolfram by entering
for the x coordinate
sum 1/n*cos((n-1)pi/4)
for the y coordinate
sum 1/n*sin((n-1)pi/4)
but they are rather messy.
https://www.desmos.com/calculator/kea5tzvijp
The z slider make pi/z the angle of rotation in radians (z=4 for this puzzle)
The b slider gives the number of terms to sum.
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Posted by Jer
on 2024-12-07 12:47:35 |
Exact solution plus a cool graph
