The plot of the equation cos(x+y)=cos(x)+cos(y) looks like a collection of infinitely many identical closed shapes.
Find the area of one of these closed shapes.
(In reply to
Solution by Brian Smith)
Using Wolfram Alpha to solve for y in Brian's rotated form, but not shrunk and then to find the integral of one particular curve:
integral_(-1.691486952)^1.691486952 sqrt(2) (0 π + cos^(-1)(-1/2 cos(sqrt(2) x) sec(x/sqrt(2)))) dx = 7.8687
For some reason WA showed the limits of integration as (-1.691486952)^1.691486952; I have no idea why. Our standard has been {-1.691486952 to 1.691486952}, making it
integral{-1.691486952 to 1.691486952} sqrt(2) (0 π + cos^(-1)(-1/2 cos(sqrt(2) x) sec(x/sqrt(2)))) dx = 7.8687
The limits of integration were from my calculation of the minor axis of one cup. The zero times pi is a substitution of 0 for an arbitrary integer n in the WA solution that gives multiple values for the repeated shapes.
Twice that value (to get the lower half) is 15.7374, in agreement with Brian Smith's value.
Can it be that the shape is so close to an ellipse, but not exactly an ellipse? ... or did we lose some precision along the way?
Also why does WA truncate at 5 significant digits?
Edited on August 10, 2020, 7:38 am
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Posted by Charlie
on 2020-08-10 07:31:54 |
re: Solution
