Possible equation for this graph?

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The discussion revolves around finding a parametric equation for a specific graph, with the horizontal axis represented by (i hat) and the vertical axis by (j hat). The proposed function is g(n) = sin(n*pi/31)*(i hat) + (sin(2*pi*n/31)+n/10)*(j hat). Participants explore the characteristics of this equation and its implications for the graph's shape. The focus is on the mathematical formulation and its potential applications. Overall, the conversation emphasizes the importance of understanding parametric equations in graphing functions.
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What could be the equation (probably parametric) for this graph?

Screen Shot 2012-01-22 at 12.21.43 PM.png
 
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Let the horizontal axis be denoted by (i hat) and the vertical axis be (j hat) and call the function g(n). The function would be something like:

g(n) = sin(n*pi/31)*(i hat) + (sin(2*pi*n/31)+n/10)*(j hat)
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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