federgraph-special-sample-maxima

/* federgraph-special-sample-maxima
   see federgraph.blogspot.de
*/

kill(all)$

a1: (x-x1)^2 + (y-y1)^2$
a2: (x-x2)^2 + (y-y2)^2$
a3: (x-x3)^2 + (y-y3)^2$

t1: sqrt(a1)$
t2: sqrt(a2)$
t3: sqrt(a3)$

f1: (t1-l)$
f2: (t2-l)$
f3: (t3-l)$

u1: f1 * (x-x1) / t1$
u2: f2 * (x-x2) / t2$
u3: f3 * (x-x3) / t3$

v1: f1 * (y-y1) / t1$
v2: f2 * (y-y2) / t2$
v3: f3 * (y-y3) / t3$

u: u1 + u2 + u3$
v: v1 + v2 + v3$

z: sqrt(u^2 + v^2);

/* equilateral triangle with side length a
   h = height
   ro = outer circle
   ri = inner circle
*/

/* side length of triangle defined */
a: 100$

h: sqrt(3)/2 * a$
ri: sqrt(3)/3 * a$
ro: sqrt(3)/6 * a$

/* constant triangle coordinates */
x1: -ri$
x2: -ri$
x3: ro$
y1: -a/2$
y2: a/2$
y3: 0$

/* Parameter l is the original length of the springs.
   All springs have the same original length.
   We are exploring a special case where the minimum for z
   touches the floor. It value of l is between 83 and 84.
   But what is the exact value of l in terms of a?
   ===============================================
   And what is the x-value of the touchdown?
*/
l: 83.5$

/* We examination of a cross section through surface. */
y: 0$

/* The cross section  gives us a 2D plot for the special case. */
plot2d(z, [x, -100, 100])$