n*sin(pi/n)*[2-cos(pi/n)]

Rectangle.

0<prime(x)<n*sin(pi/n),0<prime(y)<[2-cos(pi/n)]

The first arc in the rectangle.

prime(y)>1-sqrt(1-[prime(x)-sin([pi/n])]^2),prime(y)<1-cos(pi/n)+prime(x)*cot(pi/n),prime(y)<1+cos(pi/n)-(prime(x)*cot(pi/n))

The low row of arcs.

function(a,k,t)=[if([2*k-1]*sin([pi/n])+sin([2*pi/n*t-pi/n]),n>2*k-2)]

vector(prime(x),prime(y))=vector(function(a,k,t),1-cos([2*pi/n*t-pi/n])),k=set(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30)

The high row of arcs.

function(b,k,t)=[if([2*k]*sin([pi/n])+sin([2*pi/n*t-pi/n]),n>2*k-1)]

vector(prime(x),prime(y))=vector(function(b,k,t),1-cos([pi/n])+cos([2*pi/n*t-pi/n])),k=set(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30)

The lines with right slope.

function(c,k,t)=[if([2*k-1]*sin([pi/n])-(t*sin(pi/n)),n>2*k-3)]

vector(prime(x),prime(y))=vector(function(c,k,t),1-(t*cos(pi/n))),k=set(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)

The lines with left slope.

function(d,k,t)=[if([2*k-1]*sin([pi/n])+t*sin(pi/n),n>2*k-2)]

vector(prime(x),prime(y))=vector(function(d,k,t),1-(t*cos(pi/n))),k=set(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30)

The circle.

r=1

The radians.

theta=pi*[(2*k+1)/n+3/2],k=set(0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59)

The first arc in the circle.

y>-sqrt(1-x^2),y<x*cot(pi/n),y<-(x*cot(pi/n))

Graph of the formula

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