<p> plot(data,a,b,c) </p>

551e5924-2b55-4abb-a37e-84c981929799 44 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

Part 0: Geometrics from vector maths

3 appVersion 0.98.6179 ≡

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

N r Poly n 1 N 1 + (range z n el r i 2 * π N / * n * exp * : for z Re z Im augment 21 line :

N 7 : r 1 : 12 mat

Display only N r Poly 0.6235 0.7818 0.2225 - 0.9749 0.901 - 0.4339 0.901 - 0.4339 - 0.2225 - 0.9749 - 0.6235 0.7818 - 151015 -^* 0.6235 0.7818 82 mat

xy N r Poly :

spool to file

CWD C:\SmathFile CurrentDirectory :

data UnestCol v data 1 el : j 2 data cols range v v data j el augment : for v 31 line :

xy CWD nPoly wfile 1

data CWD nPoly rfile :

XY data UnestCol :

Circle definition t u D u 2 el u 1 el - 21 mat :

radius 1 :

pts XY . 14 black plot :

t0 0 : t1 2 π * : n 360 : 31 line

IC 0 radius 21 mat :

Text 0.75 1 start 12 black 10 end 12 green 25 mat :

s IC t0 t1 n t u D rkfixed : U s 2 col : V s 3 col : SOL U V augment : 41 line

N r Poly SOL pts Text 4 1 sys

Part 1: Geometrics from vector maths

n 5 :

d 2 :

P 02 matrix : ii 1 n 1 + (range φ 360 ° * ii n / * d * : P P φ sin φ cos 12 mat stack : 21 line for 21 line

P 0.587785252292473 0.809016994374947 - 0.951056516295154 - 0.309016994374947 0.951056516295154 0.309016994374948 0.587785252292473 - 0.809016994374948 - 4.89842541528951 1016 -^* - 1 0.587785252292474 0.809016994374947 - 62 mat

shadow in context
wrt i [imaginary] 0.951057 i 0.309017 * + arg 0.587785 i 0.809017 * - arg 21 mat ° 1854 - 21 mat

δ 18 ° * 54 ° * + (: ° 72

pointes P . 14 red plot :

P pointes 0 0.75 θ 36° 12 black 1 5 mat 0.5 0.125 - δ 72° 12 black 1 5 mat 0.5 - 0.625 - φ 36° 12 black 1 5 mat 5 1 sys

V 0 0.25 0 0.25 - 22 mat :

H 0.25 - 0 0.25 022 mat :

plot P 1212 submatrix P 2312 submatrix P 3412 submatrix P 4512 submatrix P 5612 submatrix 51 sys :

Two pairs of coordinates are required to plot a line. The 3rd pair will add the next line

plot

Common polygons d=2 36 ≡ (Triangle ≡ 5 Star ≡ 7 Hugly star ≡ 8 Losange ≡ 10 Pantagon ≡ 12 Octogon ≡ 14 Heptagon ≡ 16 Hexagon ≡ 18 Nonagon ≡ 20 Decagon ≡ 22 Hendecagon ≡ 24 Dodecagon ≡ 121 line

How it works:

The command 'matrix(0,2)' is a virtual creation, i.e: it creates a vector of 2 cols awaiting each row/col being filled with calculated values, in this case: each sin(φ) cos(φ) as they are calculated on the descending "for loop" and stacked in P at each step.

n 18 :

observe: d [1, 2, 3, 4 ... 11] d 3 :

P 0 : P 02 matrix : ii 1 n 1 + (range φ 360 ° * ii n / * d * eval : P P φ sin φ cos 12 mat stack : 21 line for 31 line

vertices P . 14 red plot :

P vertices 2 1 sys

isolate P P :

P rows 19

Export/manipulate the short form example

CWD C:\SmathFile CurrentDirectory :

P CWD Polygon wfile 1

P CWD Polygon rfile :

j 7 :

sub P 1 j range 12 range el :

j 17 range (≡ (j 916 range (≡ (|

Poly sub . 14 red plot :

sub Poly 2 1 sys

sub 0.866 0.5 0.866 0.5 - 3.231 1015 -^* 1 - 0.866 - 0.5 - 0.866 - 0.5 3.308 1015 -^* 1 0.866 0.5 72 mat

x sub 1 col : y sub 2 col : 12 mat

Area Polygon wrt vertices coordinates A 12 / x j el y j 1 + el * x j 1 + el y j el * - (j 1 x rows 1 - sum * abs : 2.598

Perimeter  Polygon wrt vertices coordinates P x j 1 + el x j el - (2^y j 1 + el y j el - (2^+ sqrt j 1 x rows 1 - sum : 6

https://www.academia.edu/24047202/COMMON_FORMULAE_FOR_REGULAR_STAR_POLYGON

72 ° *

Star 0.587785 0.809017 - 0.951057 - 0.309017 0.951057 0.309017 0.587785 - 0.809017 - 4.898425 1016 -^* - 1 0.587785 0.809017 - 62 mat :

v1 0.951057 0.309017 0.587785 - 0.809017 - 22 mat :

v2 01 0.587785 0.809017 - 22 mat :

v1 1 col v1 2 col Intercept v1 1 col v1 2 col Slope 21 mat 0.382 - 0.727 21 mat

p 5 : q 2 : 12 mat

circumradius r p 2 q * - 2 p * / π * sin 2 q * p / π * sin / eval : 0.526

v2 1 col v2 2 col Intercept v2 1 col v2 2 col Slope 21 mat 1 3.078 - 21 mat

0.951057 i 0.309017 * + arg 0.587785 i 0.809017 * - arg 21 mat ° 1854 - 21 mat

δ 18 ° * 54 ° * + (: ° 72

x f 0.382 - 0.727 x * + : x q 1 3.078 x * - : 21 sys

X x f x q - x 0.25 0.5 solve : 0.363206307490144

X f 0.118 -

star 0.587785252292473 0.809016994374947 - 0.951056516295154 - 0.309016994374947 0.951056516295154 0.309016994374948 0.587785252292473 - 0.809016994374948 - 4.89842541528951 1016 -^* - 1 0.587785252292474 0.809016994374947 - 62 mat :

U star 32 el X + 3 / : V star 32 el : 12 mat

α 0.52762076138014 :

x r circ 1 α r 2^(* x 2^- sqrt * ± :

0 r circ 0.38187798026523 0.38187798026523 - 21 sys

X f r circ 2 el X + 0.000000000000000

circXY U - V U V X X f 00 r circ 2 el X - X f 52 mat : 0.224074 - 0.309017 0.224074 0.309017 0.363206 0.117949 - 0 0.381878 - 0.363206 - 0.117949 - 52 mat

a star 11 el :

Star x r circ circXY . 14 black plot pointes a - star 1 2 el a star 1 2 el 2 2 mat 0 0.75 - a 12 red 1 5 mat 6 1 sys v1 v2 2 1 sys x f x q X X f + 20 black 1 5 mat 3 1 sys