On 29 Nov., 05:10, "Jon G." <jon8...@peoplepc.com> wrote:
> I can't help it if the news reader doesn't accept Rich Text format.  This was done in Courier.
>
> Equation of plane of n dimensions
>
>  n
> SUM a[p]x[p]=0
> p=0
>
> Normal to plane
>
> N=(a[0],a[1],a[2],...,a[n])
>
> Equation of space curve of n dimensions
>
> T=(t,t^2,t^3,...,t^n)
>
> Point on plane
>
> P=(1,1,1,...,(-a[0]-a[1]-a[2]-...-a[n-1])/a[n] )
>
> Shortest vector from origin to plane
>
>     P*N
> Q= ------N = (q[1],q[2],q[3],...,q[n])
>    |N|^2
>
> Vector in plane
>
> P[1]=P-Q
>
> Projection
>
>        (T-Q)*P[1]
> T[1] = ----------P[1]
>          |P[1]|
>
> Equation of circle on plane
>
> |P-Q|^2 = (x[1]-q[1])^2 + (x[2]-q[2])^2 + (x[3]-q[3]^2 + ....
> ... + (-a[1]x[1]-a[2]x[2]-a[3]x[3]- ... -a[n-1]x[n-1] )/a[n] - q[n] )^2
>
> Other vectors in plane
>
> n=odd
>
>   P[1]*P[b]
> ------------ = cos(2pib/n) && P[b]*N=0  b=2,3,4,...,n-1
> |P[1]||P[b]|
>
> n=even
>
>   P[1]*P[b]
> ------------ = cos(2pib/(n-1) ) && P[b]*N=0  b=2,3,4,...,n
> |P[1]||P[b]|
>
> Projections
>
>        (T-Q)*P[r]
> T[r] = ----------P[r]   r=1,2,3,...,n
>         |P[r]|^2
>
> Solution
>
> T = Q + T[1] + T[2] + T[3] + ... + T[n]


You end with a solution but I cannot see what part of your post is the
original problem, especially since you seem to abhorr verbs.