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These are answers submitted by dcasimir

You said there was the presumption that rotating a line by 90 degrees makes it normal to the original.

Is Euclid to blame for that presumption?


Is their a purely algebraical derivation?

Is this interpretation of your hint correct?

tan(phi) gives the slope of an original hypotenuse.

tan(phi+Pi/2) gives the slope of the rotated hypotenuse so that it's perpendicular to the original hypotenuse.

Their product is -1.



Alec Thanks,


However, why for the cumulative distributions did you multiply 0.445 and 0.555 by ten for the case of ten tosses and also multiplied them by 100 for the case of 100 tosses?

Is that just proper Maple syntax?



Thanks for the routine. 

I was asked to do it by hand first to fully grasp the concepts, etc.  However I'll definitely use your routine as a check.


Thanks for the suggestion.

Lately however,  I've been having not so good experiences when trying to use the maple editor (Maple Tag) when posting.

sort of leads to me using it less and less.




Here's a link to the solution. I'm having trouble including the pdf in the original post. 

Was trying to use the Mapleprimes filemanager.


Think I may have partially answered my question.

Found the orthopoly package.

anymore suggestions welcomed.

Thanks a lot.

I'm embarrassed.  I bet this is a standard example in some Linear Algebra text somewhere.


It is a 7*Pi^5.

I think that there was a misprint of the limits in the problem.

Thanks for pointing that out.



Sorry it's an integral

Int((sin(x)/x)^2, x=-infinity..infinity) = Pi/2

John, I'm sorry, I misprinted the problem. The first initial condition is N[1](0) = N[0]. I also brute forced my way through maple's DE Solver and came up with what I think is the answer. Sorry about the long delay in replying,(Christmas and New Year's) I'ts still amazing you came up with all that helpful stuff even with a misprinted question.
x(t=0) = 0 is also another initial condition in the previous problem. It didn't show up in the previous maple tags. sorry
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