Author: 藍邦偉　老師

顯示:座標軸

$x=%v$

1

-1

x

$假設建築師設計了一堵具有拋物線型垛的梭形牆，\;如圖牆的寬度為2公尺，\;沿其寬面設立x軸令原點在$
$中點且單位為公尺，\;在-1≤x≤1時，\;牆的厚度為0.6(1-x²)公尺，\;而高度為1.2+0.5(1-x²)公尺，\;$
$試求此牆的體積.$

O = (7.727407407407403, 2.459259259259246)
α = 3.7699111843077517 rad (slider from 0*° to 6.283185307179586, step 0.017453292519943295)
β = 1.3264502315156905 rad (slider from 0*° to 6.283185307179586, step 0.017453292519943295)
X_{unit}: O + (cos(α), sin(α) * cos(β))
Y_{unit}: O + (-sin(α), cos(α) * cos(β))
Z_{unit}: O + (0, sin(β))
u = Vector(O, X_{unit})
v = Vector(O, Y_{unit})
w = Vector(O, Z_{unit})
L_{Axis} = 6 (slider from 1 to 10, step 1)
u_L = Vector(O - L_{Axis} * u, O + L_{Axis} * u)
v_L = Vector(O - L_{Axis} * v, O + L_{Axis} * v)
w_L = Vector(O - L_{Axis} * w, O + L_{Axis} * w)
c = false
a = CurveCartesian(x(O + t * u + 0.6 * (1 - t^(2)) * v), y(O + t * u + 0.6 * (1 - t^(2)) * v), t, -1, 1)
b = CurveCartesian(x(O + t * u + (1.2 + 0.5 * (1 - t^(2))) * w), y(O + t * u + (1.2 + 0.5 * (1 - t^(2))) * w), t, -1, 1)
d = CurveCartesian(x(O + t * u + 0.6 * (1 - t^(2)) * v + (1.2 + 0.5 * (1 - t^(2))) * w), y(O + t * u + 0.6 * (1 - t^(2)) * v + (1.2 + 0.5 * (1 - t^(2))) * w), t, -1, 1)
e = Segment(O + u, O + u + 1.2 * w)
f = Segment(O - u, O - u + 1.2 * w)
g = Segment(O + u, O - u)
list1 = Sequence(Segment[O + t * u + 0.6 * (1 - t^(2)) * v + (1.2 + 0.5 * (1 - t^(2))) * w, O + t * u + 0.6 * (1 - t^(2)) * v], t, -1, 1, 0.1)
list4 = Sequence(Segment[O + t * u + 0.6 * (1 - t^(2)) * v + (1.2 + 0.5 * (1 - t^(2))) * w, O + t * u + (1.2 + 0.5 * (1 - t^(2))) * w], t, -1, 1, 0.02)
t = -0.1 (slider from -1 to 1, step 0.01)
poly1, h, i, j, k = Polygon(O + t * u, O + t * u + 0.6 * (1 - t^(2)) * v, O + t * u + 0.6 * (1 - t^(2)) * v + (1.2 + 0.5 * (1 - t^(2))) * w, O + t * u + (1.2 + 0.5 * (1 - t^(2))) * w)
l = PolyLine(O + t * u, O + t * u + 0.6 * (1 - t^(2)) * v, O + t * u + 0.6 * (1 - t^(2)) * v + (1.2 + 0.5 * (1 - t^(2))) * w, O + t * u + (1.2 + 0.5 * (1 - t^(2))) * w, O + t * u)
A: O + u
B: O - u
C: O + t * u
list2 = Sequence(Segment[O + t * u + 0.6 * (1 - t^(2)) * v, O + t * u], t, -1, 1, 0.1)
m = Vector(O - L_{Axis} * u, O + L_{Axis} * u)
text1: "$目前:x=" + (LaTeX[t]) + "$
$牆厚0.6(1-x^2)=" + (LaTeX[0.6 * (1 - t^(2))]) + "$
$牆高1.2+0.5(1-x^2)=" + (LaTeX[1.2 + 0.5 * (1 - t^(2))]) + "$"