x = A*cos(t) , y = A*sin(t) , z = B*t Equations for a helix that has a radius of "A" and rises by 2*pi*B units per turn "B" could also be the the pitch (distance between threads on a bolt"), it is the change in height of the helix after one full rotation. You can parameterize the equation and get r(t) = A*cos(t)i + A*sin(t)j + B*tk , where i,j,&k are vectors "t" is in radians and is equated to the angular revolution as you progress along the helix. So if you where to make two full circles around your helix then t = 4*pi. If your helix was centered around the position (0,0,0) and it had a radius of 4, then at t=0 your (x,y,z) location would be (4,0,0). If you then made two full circles around the helix your (x,y,z) location would be (4,0,4*pi)
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No shape is mathematical really unless it has been created by a mathematical formula, but is certainly a geometric shape. But anything which is a 2D or 3D shape is geometric. My improvement: A catenary curve from a mathematical equation such as cosh x, is a mathematical and natural shape. Maby each other arch can be approximated by a mathematical formula.
A spiral is first defined as a flat figure. Sometimes it is used to describe a three dimensional case.
A Rugby ball
Without an equality sign the given terms can't be considered to be an equation but if you mean 3d = -81 then the value of d works out as -27 by eliminating the 3 and dividing it into -81
D + 3D = 240 4D = 240 Divide both sides of the equation by 4: D = 60