x

Sheet Length

Sheet Width

x =

x

x

x

x

x

x

x

x

x

a = 4.625 (slider from -0.25 to Min[SheetLength / 2, SheetWidth / 2], step 0.025)
A = (-2.9, 3.94)
B = Point(Circle[A, a])
b = Segment(A, B)
SheetLength = 16
SheetWidth = 16
C = Point(Circle[B, SheetLength - 2 * a])
c = Segment(B, C)
D = Point(Circle[C, a])
d = Segment(C, D)
inputBox1 = Textfield(SheetLength)
inputBox2 = Textfield(SheetWidth)
E: (x(A), y(A) + a)
F: (x(E), y(E) + SheetWidth - 2 * a)
G: (x(F), y(F) + a)
e = Segment(A, E)
f = Segment(E, F)
g = Segment(F, G)
H: (x(B), y(B) + SheetWidth)
I: (x(C), y(C) + SheetWidth)
J: (x(D), y(D) + SheetWidth)
h = Segment(G, H)
i = Segment(H, I)
j = Segment(I, J)
L: (x(D), y(D) + a)
K: (x(L), y(L) + SheetWidth - 2 * a)
k = Segment(J, K)
l = Segment(K, L)
m = Segment(L, D)
poly1, g_1, f_1, n, p, M, N = Polygon(G, F, 4)
poly2, a_1, b_1, q, r, O, P = Polygon(A, B, 4)
poly3, c_1, d_1, s, t, Q, R = Polygon(C, D, 4)
poly4, k_1, j_1, e_1, h_1, S, T = Polygon(K, J, 4)
U: (x(D) + 4, y(D) + 2.5)
V: (x(U) + SheetLength - 2 * a, y(U))
W: (x(U), y(U) + a)
X: (x(V), y(V) + a)
i_1 = Segment(U, V)
l_1 = Segment(V, X)
m_1 = Segment(X, W)
n_1 = Segment(W, U)
Y: (x(W) + (SheetWidth - 2 * a) / 3^(0.5), y(W) + (SheetWidth - 2 * a) / 2)
Z: (x(Y) + SheetLength - 2 * a, y(Y))
AA: (x(Y), y(Y) - a)
BB: (x(Z), y(Z) - a)
p_1 = Segment(W, Y)
q_1 = Segment(Y, Z)
r_1 = Segment(Z, X)
s_1 = Segment(Z, BB)
t_1 = Segment(V, BB)
a_2 = Segment(U, AA)
b_2 = Segment(AA, Y)
c_2 = Segment(AA, BB)
inputBox3 = Textfield(a)
d_2 = Segment(M, T)
e_2 = Segment(M, O)
f_2 = Segment(O, R)
g_2 = Segment(R, T)
Vol(x) = x * (SheetLength - 2 * x) * (SheetWidth - 2 * x)
CurrentVolume: (a, a * (SheetLength - 2 * a) * (SheetWidth - 2 * a))
Xfinal = Min(SheetLength / 2, SheetWidth / 2)
A_1: (x(A), y(A) - 2)
B_1: (x(A_1) + SheetLength, y(A_1))
h_2 = Segment(A_1, B_1)
text9: "" + SheetLength + ""
C_1: (x(A) - 2, y(A))
D_1: (x(C_1), y(C_1) + SheetWidth)
i_2 = Segment(C_1, D_1)
text10: "" + SheetWidth + ""
text12: "" + SheetLength + "-2x"
text13: "" + SheetWidth + "-2x"
TG = false
text14 = If(TG, "Hide Dimensions", "Show Dimensions")
SM = false
text15 = If(SM, "Hide Max Coord", "Show Max Coord")
MaxPt = Max(Vol, 0, Min[SheetLength / 2, SheetWidth / 2])
text16: "The maximum of the volume function occurs at " + MaxPt + ".
Therefore the Maximum volume of " + (y(MaxPt)) + " occurs when " + (x(MaxPt)) + " 
is cut off from each corner."