Articles containing proofs | Space-filling polyhedra | Zonohedra | Prismatoid polyhedra
In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square. In Euclidean geometry, the four concepts—parallelepiped and cube in three dimensions, parallelogram and square in two dimensions—are defined, but in the context of a more general affine geometry, in which angles are not differentiated, only parallelograms and parallelepipeds exist. Three equivalent definitions of parallelepiped are * a polyhedron with six faces (hexahedron), each of which is a parallelogram, * a hexahedron with three pairs of parallel faces, and * a prism of which the base is a parallelogram. The rectangular cuboid (six rectangular faces), cube (six square faces), and the rhombohedron (six rhombus faces) are all specific cases of parallelepiped. "Parallelepiped" is now usually pronounced /ˌpærəˌlɛlɪˈpɪpɪd/ or /ˌpærəˌlɛlɪˈpaɪpɪd/; traditionally it was /ˌpærəlɛlˈɛpɪpɛd/ PARR-ə-lel-EP-ih-ped in accordance with its etymology in Greek παραλληλεπίπεδον parallelepipedon, a body "having parallel planes". Parallelepipeds are a subclass of the prismatoids. (Wikipedia).
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From playlist Science Unplugged: Parallel Universes
What are the properties that make up a parallelogram
👉 Learn how to solve problems with parallelograms. A parallelogram is a four-sided shape (quadrilateral) such that each pair of opposite sides are parallel and are equal. Some of the properties of parallelograms are: each pair of opposite sides are equal, each pair of opposite sides are pa
From playlist Properties of Parallelograms
Using the properties of parallelograms to solve for the missing diagonals
👉 Learn how to solve problems with parallelograms. A parallelogram is a four-sided shape (quadrilateral) such that each pair of opposite sides are parallel and are equal. Some of the properties of parallelograms are: each pair of opposite sides are equal, each pair of opposite sides are pa
From playlist Properties of Parallelograms
What are parallel lines and a transversal
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
What are the Angle Relationships for Parallel Lines and a Transversal
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
What are Parallel Lines and Parallel Planes? | Don't Memorise
Are parallel lines simply lines which do not meet? ✅To learn more about Parallel Lines, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=HdNCiP5znT8&utm_term=%7Bkeyword%7D In this video, we will learn:
From playlist Parallel Lines
I introduce the Properties of Parallelograms...the opposite sides are equal, the opposite angles are equal, the consecutive angles are supplementary, and the diagonals bisect each other. I work through four algebraic examples in this video at 4:28 14:30 Find free review test, useful notes
From playlist Geometry
What is the Consecutive Interior Angle Converse Theorem
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
Volume of the parallelepiped determined by vectors (KristaKingMath)
► My Vectors course: https://www.kristakingmath.com/vectors-course Learn how to find the volume of the parallelepiped given three vectors. ● ● ● GET EXTRA HELP ● ● ● If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com
From playlist Calculus III
Volume of a Parallelepiped using Scalar Triple Product
We start by explaining the math behind the volume of a parallelepiped which involves Cross Product and Dot Product. The volume formula is given at 9:41 Example 1) Determine the position vector of one vertex 10:11 Example 2) Find the Volume of a Parallelepiped 15:20. I will catch that my
From playlist Vector Math Lessons
Volume of the parallelepiped with adjacent edges (KristaKingMath)
► My Vectors course: https://www.kristakingmath.com/vectors-course Learn how to find the volume of the parallelepiped given adjacent edges defined by four coordinate points. ● ● ● GET EXTRA HELP ● ● ● If you could use some extra help with your math class, then check out Krista’s website
From playlist Calculus III
Multivariable Calculus: Find the volume of the parallelepiped based at the origin with adjacent sides as position vectors (1,2,3), (1,0,2), and (0,5,6). This provides an application of the triple product. For more videos like this one, please visit the Multivariable Calculus playlist
From playlist Calculus Pt 7: Multivariable Calculus
This video explains how to determine the volume of a parallelepiped using the triple scalar product. http://mathispower4u.yolasite.com/
From playlist Vectors
Diagonal Lengths of a Parallelepiped
Multivariable Calculus: Consider the parallelepiped in R^3 based at the origin with adjacent edges given by the vectors u = (1,1,-1), v=(1,2,2) and w=(2,2,0). Find the lengths of the 4 space diagonals.
From playlist Calculus Pt 7: Multivariable Calculus
Linear Algebra 14TBD: Calculation of Areas and Volumes by the Determinant
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 2 Linear Algebra: An In-Depth Course with a Focus on Applications
Geometry - Scalar Triple Product: Oxford Mathematics 1st Year Student Lecture
To give an insight in to life in Oxford Mathematics we are greatly increasing the number of undergraduate lectures that we are making available. This Geometry lecture from Professor Derek Moulton is taken from his First Year course. This course revisits some ideas encountered in high scho
From playlist Oxford Mathematics 1st Year Student Lectures
Mathematical Ideas in Lattice Based Cryptography - Jill Pipher
2018 Program for Women and Mathematics Topic: Mathematical Ideas in Lattice Based Cryptography Speaker: Jill Pipher Affiliation: Brown University Date: May 21, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Proving Parallel Lines with Angle Relationships
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
What's a Parallelogram? Geometry Terms and Definitions
An introduction to the parallelogram, a fundamental geometric shape. Geometer: Louise McCartney Artwork: Kelly Vivanco Director: Michael Harrison Written & Produced by Kimberly Hatch Harrison and Michael Harrison ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www
From playlist Socratica: The Geometry Glossary Series
Defining the Cross Product from Scratch
The cross product takes in two vectors and returns a vector orthogonal, or perpendicular, to both of them. Such a clean and simple property, however, is usually mired in its daunting formula. In this video, I show how one might think to define an operation that would return a vector orthog
From playlist Fun