e9feebd4-70a0-4169-93f7-9ce7c6ca48b0 14 4 5 false false 0 decimal

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

xC yC R circleCR Δθ π 24 / : k 12 π * Δθ / 1 + (range : z k el R e i Δθ * k *^* : z Re xC + z Im yC + augment eval 41 line :

x f1 x 1 x 1 - 22 mat :

H.L 0.2 :

H.W 0.2 :

SP.x SP.y L.v α Arrow 00 L.v 0 L.v H.L - H.W 2 / L.v H.L - H.W 2 / - L.v 052 mat α cos α sin α sin - α cos 22 mat * (SP.x SP.y SP.x SP.y SP.x SP.y SP.x SP.y SP.x SP.y 52 mat + :

SP.x 0 :

SP.y 0 :

L.v 1 :

α 310 ° * :

Text 0.5 0.5 D 15 red 0.35 0.25 - R 15 blue 25 mat :

2 f u v pRegion M 0 : n 0 : 12 mat r 1 u length range c 1 v length range u r el v c el f n n 1 + : M n 1 el u r el : M n 2 el v c el : 13 mat continue if for for M eval 31 line :

a b N pR d b a - N 1 - / : R 0 : 12 mat n 1 N range R n el a n 1 - (d * + : for R 31 line :

R 1 :

N 60 :

This problem is very old, but with a horse and a rope (who use a chain?). I remember this as the solution given by my dad. For a guy how use just a calc ruler a lot of year, it's very good. And I can't solve it, in those days. The symbolic solution was published at my faculty a couple of weeks later. Alvaro

D R 60 ° * sin / : 1.1547

Curves

C.1 x 2^y 2^+ R 2^- :

C.2 x R - (2^y 2^+ D 2^- :

x y C 0 > x y Point is_outside * x y C 0 < x y Point is_inside * x y C 0 ≡ x y Point is_in_C * cases

Regions

x y Ρ.1 C.1 0 < (C.2 0 < (x 0 < (& (& :

x y Ρ.2 C.1 0 < (C.2 0 > (x 0 > (& (& :

0 0 R circleCR R 0 D circleCR SP.x SP.y L.v α Arrow R SP.y D 125 ° * Arrow Text 0 f1 x y Ρ.1 0.5 - 0 N pR 0.75 - 0.75 N pR pRegion . 4 red augment x y Ρ.2 0 0.5 N pR 1 - 1 N pR pRegion . 4 green augment 8 1 sys

Using create mesh

2 f a b c d n.x n.y Hatch x y Clear x y A x y f x y 031 mat * : M x# y# A a b c d n.x n.y CreateMesh : M 1 col M 2 col augment 41 line :

0 0 R circleCR R 0 D circleCR SP.x SP.y L.v α Arrow R SP.y D 125 ° * Arrow Text 0 f1 x y Ρ.2 0.5 - 0.5 1 - 1 N N Hatch . 4 green augment x y Ρ.1 0.5 - 0 0.6 - 0.6 N N Hatch 8 1 sys