Undergrad What is the formula for plotting an accelerating involute curve?

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The discussion focuses on finding a formula for plotting an accelerating involute curve. Participants express confusion about the term "accelerated" and the necessary context for deriving the curve. A referenced wiki provides general formulas for involute curves, but users struggle to decipher how to apply them for their specific needs. It is suggested that a parametric plot may be required to visualize the curve effectively. The conversation emphasizes the need for clarity in defining the parameters and context for plotting the accelerating involute.
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I once viewed an involute which the involute accelerated.
Can someone help me with a formula for an accelerating involute curve? I have found this wiki on involute
 
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What do you mean by "accelerated"?

It looks like there is a lot of context missing.
 
The circle of derivation is increasing as the "string" around that circle is enlarging
 
homerwho said:
Summary: I once viewed an involute which the involute accelerated.

Can someone help me with a formula for an accelerating involute curve? I have found this wiki on involute
This wiki page you cited has a formula for a general curve, and several more for specific types of curves. Isn't one of these what you're looking for?
 
possibly. that's why I posted in the math forum. I can't decipher from that what I would need to plot. Thanks
 
homerwho said:
possibly. that's why I posted in the math forum. I can't decipher from that what I would need to plot. Thanks
For most of the formulas on the page you linked to, you need to do a parametric plot. For example, to plot ##x(t) = t + \sin(t), y(t) = 3 + \cos(t)## on the interval ##[0, 2\pi]##, you can do this in WolframAlpha:

parametric plot (t + sin t, 3 + cos t), t=0..2pi

Here's a link to the plot - https://www.wolframalpha.com/input/?i=parametric+plot+(t+++sin+t,+3+++cos+t),+t=0..2pi
 
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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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