11,000+
Interactive Demonstrations Powered by Notebook Technology »
TOPICS
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Intersection of a Plane and a Tetrahedron
Let
be a tetrahedron and let
and
be the midpoints of the edges
and
. Let a plane that contains the line
intersect the edges
and
at points
and
. Then
bisects
.
Contributed by:
Izidor Hafner
THINGS TO TRY
Rotate and Zoom in 3D
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
DETAILS
A proof is described in [1, p. 126].
Reference
[1] V. V. Prasolov and I. F. Sharygin,
Problems in Stereometry
(in Russian), Moscow: Nauka, 1989.
RELATED LINKS
Tetrahedron
(
Wolfram
MathWorld
)
Orthogonal Projection of a Rectangular Solid
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Izidor Hafner
"
Intersection of a Plane and a Tetrahedron
"
http://demonstrations.wolfram.com/IntersectionOfAPlaneAndATetrahedron/
Wolfram Demonstrations Project
Published: March 15, 2017
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Construct a Dihedral Angle of a Tetrahedron Given Its Plane Angles at a Vertex
Izidor Hafner
Right-Angled Tetrahedron
Izidor Hafner
Inscribed and Circumscribed Spheres of a Tetrahedron
Izidor Hafner
Monge Point of a Tetrahedron
Izidor Hafner
Altitude of a Tetrahedron Given Its Edges
Izidor Hafner
Completing a Tetrahedron to a Parallelepiped
Izidor Hafner
Dissection of Hill's Tetrahedron of Type 1
Izidor Hafner
Two Conditions for a Tetrahedron to Be Orthocentric
Izidor Hafner
Rolling a Regular Tetrahedron on a Regular Icosahedron
Izidor Hafner
A Theorem on the Dihedral Angles of a Tetrahedron
Izidor Hafner
Related Topics
3D Graphics
Polyhedra
Solid Geometry
Browse all topics