96e25127-cbd2-4821-92e3-377995a9837d 2 4 5 decimal

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Polygon Area/Perimeter

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

A method for finding the area of any polygon when the coordinates of its vertices are known

x 2064215 mat transpose :

y 0550015 mat transpose :

uv x y augment :

Area Polygon wrt vertices coordinates A 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * abs :

a b c spec . 14 red 13 mat : XY uv a b c spec pts : 21 sys

Perimeter is calculated wrt each hypotenuse from the projections ... Inspect the plot.

uv XY 2 1 sys

Perimeter  Polygon wrt vertices coordinates P x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum :

HR A P / :

N 10000 :

A P 12 mat 20 18.77 12 mat

A P HR 31 mat 20 18.77 1.066 31 mat

X 2 N 1 Random (* 1 - : Y 2 N 1 Random (* 1 - : 21 line

uv XY 2 1 sys

Fill the circle exclusive of the square Circle i 1 N range U i el X i el X i el (2^Y i el (2^+ HR < 0 cases : V i el Y i el X i el (2^Y i el (2^+ HR < 0 cases : 21 line for U V augment 21 line :

A P HR 13 mat 20 18.77 1.066 13 mat

Monte Carlo 'Pi'

Circle 2 1 sys