I.
Planes and rectangles to....
1. Two infinitely long, directly opposed parallel plates
of the same finite width.
2.
Two infinitely long parallel plates of different widths; centerlines of
plates are connected by perpendicular between plates.
3.
Two infinitely long plates of unequal widths h and w, having one common
edge, and at an angle of 90^{o} to each other.
4.
Two infinitely long plates of equal widths having a common edge and
included angle a
5.
Two infinitely long plates of unequal width having a common edge with an
included angle a
6.
Infinitely long enclosure formed by three planar or convex surfaces.
7.
Infinite plane to row of parallel cylinders, or n rows of inline
cylinders.
8.
Infinite plane to first, second, and first plus second rows of infinitely
long parallel tubes of equal diameter in equilateral triangular array.
9.
Top surface of finite rectangle tilted relative to an infinite plane.
10. Rectangles having a common edge and forming an
arbitrary angle; one rectangle infinitely long.
11. Identical, parallel, directly opposed rectangles.
12. Coaxial parallel squares of different edge length.
12a.Squares of different edge length in perpendicular planes.
One corner of square 2 touches plane containing unit square 1
13. Rectangle to rectangle in a parallel plane; all
boundaries are parallel or perpendicular to x and x boundaries.
13a. Rectangle to coaxial disk in a parallel plane.
13b. Rectangle to torus in parallel plane.
13c. Rectangle to Wshaped tube in parallel plane.
14. Two finite rectangles of same length, having one
common edge, and at an angle of 90^{o} to each other.
15. Rectangle to rectangle in a perpendicular plane; all
boundaries are parallel or perpendicular to x and x boundaries.
15a.Rectangle to disk in perpendicular plane. Disk is
symmetrically centered with rectangle, and touches rectangle center.
16. Two rectangles with one common edge and included
angle of f.
17. Rectangle 1 to rectangle 2 in a plane intersecting
the plane containing rectangle 1. All rectangle edges are parallel or
perpendicular to the line of intersection of the containing planes.
18. Finite area on interior of rectangular enclosure to
second finite area.
19. Right triangle to perpendicular rectangle with common
side.
20. Isosceles triangle to perpendicular rectangle: Base
of triangle and rectangle have common edge.
21. Right triangle with side of length onehalf that of
perpendicular rectangle to rectangle.
22. Perpendicular right triangles with one equal edge.
23. Right triangle to perpendicular right triangle with
common edge; apexes at common point.
24. Right triangle to perpendicular right triangle with
common edge; apexes at opposite ends.
25. Triangle to perpendicular rectangle.
26. Right triangle to perpendicular right triangle of
unequal size; apexes at opposite ends of shared edge.
27. Right triangle to perpendicular right triangle of
unequal size; apexes at common point.
28. Right isosceles triangle to adjacent congruent
perpendicular triangle connected along short side.
29. Parallel directly opposed right triangles.
30. Parallel directly opposed rectangles with triangular
extensions.
31. Floor to end wall with triangular extension.
32. Side wall to end wall with triangular extension.
33. Between all combinations of surfaces in a hexagonal
prism.
34. Between parallel regular polygons.
35. One side of rectangle to one quarter of parallel
cylinder of same length as rectangle; cylinder is bisected longitudinally
by plane containing rectangle.
36. Rectangle to perpendicular circular segment.
37. Horizontal panel to adjacent vertical panel with
circular segment on top.
38. Side wall to end wall with circular segment
extension.
II.
Disk to....
39. Circular disk to parallel right triangle; normal from
center of circle passes through one acute vertex.
40. Disk to parallel coaxial disk of same radius.
41. Disk to parallel coaxial disk of unequal radius.
42. Disk to second coaxial disk inside cone.
43. Nonintersecting disks with intersecting axes; axes
intersect between disks; and disks can be inscribed in sphere of radius r_{3}
(i.e., r_{1}^{2} + h_{1}^{2} = r_{2}^{2}
+ h_{2}^{2} = r_{3}^{2})
44. Nonintersecting disks with intersecting axes; axes do
not intersect between disks. Disks can be inscribed in sphere of radius r_{3}
(i.e., r_{1}^{2} + h_{1}^{2} = r_{2}^{2}
+ h_{2}^{2} = r_{3}^{2})
45. Sector of circular disk to sector of parallel
circular disk.
46. Parallel opposed circular segments.
47. Disk to coaxial annular ring on parallel disk.
48. Disk to coaxial cone.
49. Annular Disk to coaxial truncated cone; cone can be
convergent (+a) or
divergent (a).
50. Disk to a coaxial paraboloid.
51. Disk to coaxial ellipsoid.
52. Ring to parallel coaxial ring.
53. Annulus to coaxial annulus of different outer radius;
both annuli have inner radius of blocking coaxial cylinder.
54. Coaxial annular rings separated by coaxial cylinder.
55. Annular ring between two concentric cylinders to
inside of outer cylinder; inner radius of ring is equal to radius of inner
cylinder.
56. Ring on annulus between coaxial cylinders to inner
surface of outer cylinder.
57. Annular ring around base of hemisphere to hemisphere.
58. Ring around base of hemisphere to section of
hemisphere.
59. Annular ring to attached coaxial paraboloid.
60. Annular ring to attached coaxial ellipsoid.
III.
Cylinder to....
61.
Exterior of infinitely long cylinder to symmetrically placed infinitely
long parallel rectangle.
62. Exterior of infinitely long cylinder to
unsymmetrically placed infinitely long parallel plate.
63. Concentric cylinders of infinite length.
64. Exterior of infinitely long cylinder to interior of
concentric semicylinder.
65. Interior of infinitely long semicylinder to itself
when concentric coaxial cylinder is present.
66. Interior of infinitely long semicylinder 1 to
interior of semicylinder 2 when concentric parallel cylinder 3 is present.
67. Infinitely long cylinder to nonconcentric
cylindrical enclosure.
68. Infinitely long parallel cylinders of the same
diameter.
69. Infinite parallel cylinders of different radius.
70. Infinitely long facing parallel semicylinders of
equal radius.
71. Infinitely long semicylinder to parallel infinitely
long semicylinder of same radius.
72. Infinitely long cylinder to other cylinders in square
array of parallel cylinders of equal diameter.
73. Infinitely long cylinder to other cylinders in
equilateral triangular array of parallel cylinders of equal diameter.
74. Finitelength cylinder to rectangle with two edges
parallel to cylinder axis and of length equal to cylinder.
75. Finite cylinder to finite rectangle of same length.
76. Outside surface of cylinder to perpendicular right
triangle; triangle is in plane of cylinder base with one vertex of triangle
at center of base.
77. Outer surface of cylinder to annular disk at end of
cylinder.
78. Inner surface of right circular cylinder to itself.
78a. Flat spiral tape of width h rolled around imaginary cylinder of
diameter d and length l.
78b. Long flat double helix
79. Base of right circular cylinder to inside surface of
cylinder.
80. Disk in cylinder base or top to inside surface of
right circular cylinder.
81. Inside surface of right cylinder to coaxial disk of
same diameter separated from base of cylinder.
82. Interior surface of circular cylinder of radius R to
disk of radius r where r < R; disk is perpendicular to axis of cylinder,
and axis passes through center of disk.
83. Annular ring on cylinder base or top to inside of
right circular cylinder.
84. Interior of right circular cylinder to finite annular
ring in base.
85. Inner surface of upper cylinder to base ring.
86. Inside surface of right circular cylinder to inside
surface of adjacent right circular cylinder of the same diameter.
87. Finite section of right circular cylinder to
separated finite section.
88. Interior of halfcylinder to interior of opposed
adjacent coaxial halfcylinder of equal length.
89. Coaxial right circular cylinders of different radii,
one atop the other, Case I.
90. Coaxial right circular cylinders of different radii,
one atop the other, Case II.
91. Interior of finite length right circular coaxial
cylinder to itself.
92. Interior of outer right circular cylinder of finite
length to exterior of coaxial inner right circular cylinder.
93. Interior of outer right circular cylinder of finite
length to annular end enclosing space between coaxial cylinders.
94. Annular end enclosing space between coaxial right
circular cylinders to opposite annular end.
95. Inner coaxial cylinder to outer coaxial cylinder;
inner cylinder entirely within outer.
96. Inner coaxial cylinder to outer coaxial cylinder;
inner cylinder extends beyond one end of outer.
97. Inner coaxial cylinder to outer coaxial cylinder;
inner cylinder extends beyond both ends of outer.
98. Outside of inner (smaller) coaxial cylinder to inside
of larger cylinder; small cylinder completely outside larger.
99. Between equal length cylindrical areas on interior of
outer coaxial cylinder.
100. Between cylindrical area on interior of shell and
equal length cylindrical area on exterior of inner coaxial cylinder.
101. Parallel opposed cylinders of unequal radius and
equal finite length.
102. Perpendicular cylinders of equal radius and equal
finite length, closest separation at centers.
103. Cylinders of equal radius and length, one cylinder
rotated around line joining centers.
104. Finite cylinders of equal radius and length.
Cylinders are rotated at 90^{o} from line connecting their ends.
105. Cylinders of equal length and radius, rotated around
line connecting ends.
106. Cylinder of length l/2 to perpendicular cylinder of
length l and same radius. Cylinder axes intersect at center of longer
cylinder.
107. Cylinder of length l/2 to cylinder of equal radius
and length l rotated in plane containing cylinder axes about a line through
end of longer cylinder.
108. Cylinder of length
l/2 to skewed cylinder of equal radius and length.
IV.
Cone to....
109. Interior of right circular cone to base.
110. Interior of right circular cone to itself.
111. Interior of frustum of right circular cone to base.
111a Interior of Frustum of Right Circular Cone to Itself
112. Frustum of right circular cone to entire base.
112a. Frustum of right circular cone to base with obstruction
by coaxial internal cylinder
113. Frustum of right circular cone to disk in base of
cone.
114. Frustum of right circular cone cut by plane parallel
to cone axis.
115. Finite section of right circular cone to separated
finite section.
115a. Spiral flat tape wrapped around right
circular cone.
116. Interior of frustum of right circular cone to
attached right circular cone.
117. Interior of right circular cone to base of attached
frustum.
118. Frustum of right circular cone to coaxial attached
frustum.
119. Interior of frustum of right circular cone to base
of attached coaxial frustum.
120. Cone to coaxial body of revolution (cone, paraboloid or ellipsoid).
V.
Sphere to....
121.
Sphere to rectangle perpendicular to line through sphere axis.
122. Sphere to rectangle.
122a. Sphere to plane
rectangle. Sphere lies on corner of adjacent rectangle with common side and
intersecting A_{2} at angle ø
123. Sphere to scalene triangle in
plane perpendicular to sphere axis with one vertex on axis; sphere does not
intersect plane of triangle.
124. Sphere to any polygon in plane that does not
intersect sphere.
125. Sphere to coaxial disk.
126. Sphere to noncoaxial disk; plane of disk does not
intersect sphere. Point o may lie inside or outside disk.
127. Sphere to sector on coaxial disk.
128. Sphere to segment on a coaxial disk.
129. Sphere to top of coaxial annular ring not touching
sphere.
130. Sphere to top of coaxial annular ring touching
sphere.
131. Sphere to interior surface of coaxial right circular
cylinder; sphere outside end of cylinder, and sphere radius less than
cylinder radius.
132. Sphere to interior surface of coaxial right circular
cylinder; sphere within ends of cylinder.
133. Sphere to exterior of coaxial cylinder.
134. Large sphere to small cylinder. r>> diameter
or length of cylinder.
135. Concentric spheres.
136. Differential or finite areas on the inside of a
spherical cavity.
137. Two spheres of unequal radius.
138. Sphere to spherical cap.
139. Sphere to coaxial cone.
140. Large sphere to small hemisphere (not including
circular base).
140a. Two directly opposed spherical caps on a common axis.
140b: Spherical cap on a sphere of radius r to itself and to
its base.
140c:
Two complementary spherical caps on the sphere of radius r.
140d:
Two spherical caps of different size
on the same sphere of radius r.
140e. Euclidian spherical spiral with
uniform spiral band.
140f. Logarithmic spherical spiral band.
141. Sphere to coaxial paraboloid.
142. Sphere to coaxial ellipsoid.
143. Large sphere to small ellipsoid.
144. Ring area on inside of sphere to coaxial ring area
on inside of attached frustum.
145. Ring area on inside of sphere to ring on interior of
cylinder attached to sphere by a conical frustum.
VI.
Hemisphere to....
146. Any finite area of any shape on interior of
hemisphere to entire base.
147. Spherical cap to disk in equatorial plane.
148. Interior finite section of hemisphere to itself.
149. Finite section on interior of hemisphere to parallel
finite section.
150. Section of interior of hemisphere to disk on base.
151. Finite section of interior of hemisphere to disk on
base.
152. Section of hemisphere to annular ring in base.
153. Ring on hemispherical surface to ring on the base.
154. Two hemispheres in contact.
VII.
Other
155. Moebius strip of constant width to itself.
156. Seated standard person facing vertical panel.
157. Seated standard person to side vertical rectangle.
158. Seated standard person to rectangle on ceiling or
floor.
159. Standard standing person to rectangle on ceiling.
160. Standing standard person to side vertical rectangle.
161. Standing standard person to vertical facing
rectangle.
162. Pig to rectangle in various orientations.
