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What is Space(full documentary)HD
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. In mathematics, "spaces" are examined with different numbers of dimensions and with differen
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Calculus III: Three Dimensional Coordinate Systems (Level 1 of 10)
This video is a review of number lines and coordinate systems. This video goes over the basic concepts and terminology of one dimensional, and two dimensiona...
-
Calculus III: Three Dimensional Coordinate Systems (Level 2 of 10)
This video continues the exploration of a three dimensional cartesian coordinate system. Basic equations of a two dimensional coordinate system are presented...
-
three dimensional space
Plotting and describing points in three-dimensional space.
-
Three-dimensional space
Three-dimensional space is a geometric three-parameter model of the physical universe (without considering time) in which all known matter exists. These three dimensions can be labeled by a combination of three chosen from the terms length, width, height, depth, and breadth. Any three directions can be chosen, provided that they do not all lie in the same plane.
In physics and mathematics, a seque
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Subspaces of Three Dimensional Space | MIT 18.06SC Linear Algebra, Fall 2011
Subspaces of Three Dimensional Space Instructor: Linan Chen View the complete course: http://ocw.mit.edu/18-06SCF11 License: Creative Commons BY-NC-SA More i...
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Vectors in Three Space.mp4
This video lesson shows how to do the following in three space: - graph in three dimensional space - find the components of a vector between 2 specific point...
-
Calc III Lesson 05 Lines in Three Dimensional Space.mp4
Download the pdf file of notes for this video: http://math.sci.ccny.cuny.edu/docs?name=Calc+III+Lesson+05+Lines+in+Three+Dimensional+Space.pdf For more infor...
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Coordinate Planes in Three dimensional space - Designmate
Three dimensional coordinate system and the sign convention. - Designmate.
-
How Many Dimensions Does The Universe Have?
Dimensions are complicated, and wrapping your mind around how many there are can give you a headache. Join Trace as he explains everything you should know about them.
Read More:
What is a dimension, and how many are there?
http://science.howstuffworks.com/science-vs-myth/everyday-myths/dimension.htm
"As you've probably noticed, we live in a world defined by three spatial dimensions and one
-
Space-Time And The Speed Of Light | Einstein's Relativity
http://facebook.com/ScienceReason ... Albert Einstein's Theory of Relativity (Chapter 3): Space-Time And The Speed Of Light
The concept of spacetime combines space and time to a single abstract "space", for which a unified coordinate system is chosen. Typically three spatial dimensions (length, width, height), and one temporal dimension (time) are required. Dimensions are independent components o
-
Graphs of Planes in Three-Dimensional Space
The ways that planes can interact in three-dimensional space.
-
3DS Mission 1 - Three Dimensional Space System by Hornby
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Michio Kaku: The Multiverse Has 11 Dimensions
Don't miss new Big Think videos! Subscribe by clicking here: http://goo.gl/CPTsV5 The physicist explains why other universes in the mulitverse could have man...
-
WildLinAlg11: Applications of 3x3 matrices
This is the 11th lecture in this course on Linear Algebra by N J Wildberger. Here we talk about 3x3 matrices and their applications to linear transformations of three dimensional space. This includes dilations, reflections, rotations with plenty of examples.
CONTENT SUMMARY: pg 1: @00:08 matrix/vector multiplication; Two interpretations: linear transformation/Change of coordinates; active vs pass
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Introduction to the Three Dimensional Rectangular Coordinate System
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Vectors in Three Dimensional Space - Section 8.3
This Precalculus lesson is very similar to what we did with two dimension vectors (section 8.2). Magnitude and unit vectors are included.
-
WildLinAlg9a: Three dimensional affine geometry
This is the first video of the ninth lecture of this course on Linear Algebra. Here we give a gentle introduction to three dimensional space, starting with t...
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Asiro - Three-dimensional space
Asiro - Nocturnal Asiro - Physical p l a n e Asiro - microwave beat --- https://soundcloud.com/asiroerudite http://asiroerudite.bandcamp.com/
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[Multivariable Calculus] Points and Vectors in Three Dimensional Space
In this video I go over one, two, and three dimensional space and points in those spaces. Then I quickly review the basics of vectors, including magnitude, vector addition and subtraction, scalar multiplication, and unit vectors. I also show how a point can be represented by its corresponding position vector in standard position. Lastly, I go over the standard basis vectors in three dimensional sp
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Hidden Dimensions: Exploring Hyperspace
Extra dimensions of space—the idea that we are immersed in hyperspace—may be key to explaining the fundamental nature of the universe. Relativity introduced time as the fourth dimension, and Einstein’s subsequent work envisioned more dimensions still--but ultimately hit a dead end. Modern research has advanced the subject in ways he couldn’t have imagined. John Hockenberry joins Brian Greene, Lawr
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[Multivariable Calculus] Equations of Lines in Three Dimensional Space
In this video I show how to represent a line in three dimensional space with its vector equation by finding an initial point and direction vector. I also show how to represent a line with its parametric equations and symmetric equations, and go over a quick example illustrating these points.
If you have any questions, feedback, or video requests, please leave a comment.
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WildLinAlg9: Three dimensional affine geometry
This is the ninth lecture of this course on Linear Algebra by N J Wildberger. Here we give a gentle introduction to three dimensional space, starting with th...
What is Space(full documentary)HD
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three lin...
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. In mathematics, "spaces" are examined with different numbers of dimensions and with different underlying structures. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.
Modern Physics:Gravitation:http://youtu.be/STrXFteB66Y
How The Human Mind Was Born:http://youtu.be/-9_Mo8Pxq-s
The Voyage To Pluto:http://youtu.be/ls7LWOcQfi8
Athene`s Theory of Everything:http://youtu.be/-JoaBSI0OhU
String Theory:Theory of Everything:http://youtu.be/asd617P6i2Q
Universe or Multiverse:http://youtu.be/Nuz5EtbzlUc
wn.com/What Is Space(Full Documentary)Hd
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. In mathematics, "spaces" are examined with different numbers of dimensions and with different underlying structures. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.
Modern Physics:Gravitation:http://youtu.be/STrXFteB66Y
How The Human Mind Was Born:http://youtu.be/-9_Mo8Pxq-s
The Voyage To Pluto:http://youtu.be/ls7LWOcQfi8
Athene`s Theory of Everything:http://youtu.be/-JoaBSI0OhU
String Theory:Theory of Everything:http://youtu.be/asd617P6i2Q
Universe or Multiverse:http://youtu.be/Nuz5EtbzlUc
- published: 04 Nov 2014
- views: 81550
Calculus III: Three Dimensional Coordinate Systems (Level 1 of 10)
This video is a review of number lines and coordinate systems. This video goes over the basic concepts and terminology of one dimensional, and two dimensiona......
This video is a review of number lines and coordinate systems. This video goes over the basic concepts and terminology of one dimensional, and two dimensiona...
wn.com/Calculus Iii Three Dimensional Coordinate Systems (Level 1 Of 10)
This video is a review of number lines and coordinate systems. This video goes over the basic concepts and terminology of one dimensional, and two dimensiona...
Calculus III: Three Dimensional Coordinate Systems (Level 2 of 10)
This video continues the exploration of a three dimensional cartesian coordinate system. Basic equations of a two dimensional coordinate system are presented......
This video continues the exploration of a three dimensional cartesian coordinate system. Basic equations of a two dimensional coordinate system are presented...
wn.com/Calculus Iii Three Dimensional Coordinate Systems (Level 2 Of 10)
This video continues the exploration of a three dimensional cartesian coordinate system. Basic equations of a two dimensional coordinate system are presented...
three dimensional space
Plotting and describing points in three-dimensional space....
Plotting and describing points in three-dimensional space.
wn.com/Three Dimensional Space
Plotting and describing points in three-dimensional space.
Three-dimensional space
Three-dimensional space is a geometric three-parameter model of the physical universe (without considering time) in which all known matter exists. These three d...
Three-dimensional space is a geometric three-parameter model of the physical universe (without considering time) in which all known matter exists. These three dimensions can be labeled by a combination of three chosen from the terms length, width, height, depth, and breadth. Any three directions can be chosen, provided that they do not all lie in the same plane.
In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called three-dimensional Euclidean space. It is commonly represented by the symbol . This space is only one example of a great variety of spaces in three dimensions called 3-manifolds.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video
wn.com/Three Dimensional Space
Three-dimensional space is a geometric three-parameter model of the physical universe (without considering time) in which all known matter exists. These three dimensions can be labeled by a combination of three chosen from the terms length, width, height, depth, and breadth. Any three directions can be chosen, provided that they do not all lie in the same plane.
In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called three-dimensional Euclidean space. It is commonly represented by the symbol . This space is only one example of a great variety of spaces in three dimensions called 3-manifolds.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video
- published: 30 Oct 2014
- views: 2
Subspaces of Three Dimensional Space | MIT 18.06SC Linear Algebra, Fall 2011
Subspaces of Three Dimensional Space Instructor: Linan Chen View the complete course: http://ocw.mit.edu/18-06SCF11 License: Creative Commons BY-NC-SA More i......
Subspaces of Three Dimensional Space Instructor: Linan Chen View the complete course: http://ocw.mit.edu/18-06SCF11 License: Creative Commons BY-NC-SA More i...
wn.com/Subspaces Of Three Dimensional Space | Mit 18.06Sc Linear Algebra, Fall 2011
Subspaces of Three Dimensional Space Instructor: Linan Chen View the complete course: http://ocw.mit.edu/18-06SCF11 License: Creative Commons BY-NC-SA More i...
Vectors in Three Space.mp4
This video lesson shows how to do the following in three space: - graph in three dimensional space - find the components of a vector between 2 specific point......
This video lesson shows how to do the following in three space: - graph in three dimensional space - find the components of a vector between 2 specific point...
wn.com/Vectors In Three Space.Mp4
This video lesson shows how to do the following in three space: - graph in three dimensional space - find the components of a vector between 2 specific point...
Calc III Lesson 05 Lines in Three Dimensional Space.mp4
Download the pdf file of notes for this video: http://math.sci.ccny.cuny.edu/docs?name=Calc+III+Lesson+05+Lines+in+Three+Dimensional+Space.pdf For more infor......
Download the pdf file of notes for this video: http://math.sci.ccny.cuny.edu/docs?name=Calc+III+Lesson+05+Lines+in+Three+Dimensional+Space.pdf For more infor...
wn.com/Calc Iii Lesson 05 Lines In Three Dimensional Space.Mp4
Download the pdf file of notes for this video: http://math.sci.ccny.cuny.edu/docs?name=Calc+III+Lesson+05+Lines+in+Three+Dimensional+Space.pdf For more infor...
Coordinate Planes in Three dimensional space - Designmate
Three dimensional coordinate system and the sign convention. - Designmate....
Three dimensional coordinate system and the sign convention. - Designmate.
wn.com/Coordinate Planes In Three Dimensional Space Designmate
Three dimensional coordinate system and the sign convention. - Designmate.
How Many Dimensions Does The Universe Have?
Dimensions are complicated, and wrapping your mind around how many there are can give you a headache. Join Trace as he explains everything you should know about...
Dimensions are complicated, and wrapping your mind around how many there are can give you a headache. Join Trace as he explains everything you should know about them.
Read More:
What is a dimension, and how many are there?
http://science.howstuffworks.com/science-vs-myth/everyday-myths/dimension.htm
"As you've probably noticed, we live in a world defined by three spatial dimensions and one dimension of time."
Imagining Other Dimensions
http://www.pbs.org/wgbh/nova/physics/imagining-other-dimensions.html
"For most of us, or perhaps all of us, it's impossible to imagine a world consisting of more than three spatial dimensions."
10 Dimensions
http://www.universetoday.com/48619/10-dimensions/
"We all consider dimensions in general terms such as another reality or how we perceive the environment around us."
How Many Dimensions Does the Universe Really Have?
http://www.pbs.org/wgbh/nova/blogs/physics/2014/04/how-many-dimensions-does-the-universe-really-have/
"An engineer, a mathematician and a physicist walk into a universe. How many dimensions do they find?"
Extra dimensions, gravitons, and tiny black holes
http://home.web.cern.ch/about/physics/extra-dimensions-gravitons-and-tiny-black-holes
"Why is gravity so much weaker than the other fundamental forces?"
Scientists suggest spacetime has no time dimension
http://phys.org/news/2011-04-scientists-spacetime-dimension.html
"The concept of time as a way to measure the duration of events is not only deeply intuitive, it also plays an important role in our mathematical descriptions of physical systems."
Theoretical physics: The origins of space and time
http://www.nature.com/news/theoretical-physics-the-origins-of-space-and-time-1.13613
"Many researchers believe that physics will not be complete until it can explain not just the behaviour of space and time, but where these entities come from."
____________________
DNews is dedicated to satisfying your curiosity and to bringing you mind-bending stories & perspectives you won't find anywhere else! New videos twice daily.
Watch More DNews on TestTube http://testtube.com/dnews
Subscribe now! http://www.youtube.com/subscription_center?add_user=dnewschannel
DNews on Twitter http://twitter.com/dnews
Trace Dominguez on Twitter https://twitter.com/tracedominguez
Tara Long on Twitter https://twitter.com/TaraLongest
DNews on Facebook https://facebook.com/DiscoveryNews
DNews on Google+ http://gplus.to/dnews
Discovery News http://discoverynews.com
Download the TestTube App: http://testu.be/1ndmmMq
wn.com/How Many Dimensions Does The Universe Have
Dimensions are complicated, and wrapping your mind around how many there are can give you a headache. Join Trace as he explains everything you should know about them.
Read More:
What is a dimension, and how many are there?
http://science.howstuffworks.com/science-vs-myth/everyday-myths/dimension.htm
"As you've probably noticed, we live in a world defined by three spatial dimensions and one dimension of time."
Imagining Other Dimensions
http://www.pbs.org/wgbh/nova/physics/imagining-other-dimensions.html
"For most of us, or perhaps all of us, it's impossible to imagine a world consisting of more than three spatial dimensions."
10 Dimensions
http://www.universetoday.com/48619/10-dimensions/
"We all consider dimensions in general terms such as another reality or how we perceive the environment around us."
How Many Dimensions Does the Universe Really Have?
http://www.pbs.org/wgbh/nova/blogs/physics/2014/04/how-many-dimensions-does-the-universe-really-have/
"An engineer, a mathematician and a physicist walk into a universe. How many dimensions do they find?"
Extra dimensions, gravitons, and tiny black holes
http://home.web.cern.ch/about/physics/extra-dimensions-gravitons-and-tiny-black-holes
"Why is gravity so much weaker than the other fundamental forces?"
Scientists suggest spacetime has no time dimension
http://phys.org/news/2011-04-scientists-spacetime-dimension.html
"The concept of time as a way to measure the duration of events is not only deeply intuitive, it also plays an important role in our mathematical descriptions of physical systems."
Theoretical physics: The origins of space and time
http://www.nature.com/news/theoretical-physics-the-origins-of-space-and-time-1.13613
"Many researchers believe that physics will not be complete until it can explain not just the behaviour of space and time, but where these entities come from."
____________________
DNews is dedicated to satisfying your curiosity and to bringing you mind-bending stories & perspectives you won't find anywhere else! New videos twice daily.
Watch More DNews on TestTube http://testtube.com/dnews
Subscribe now! http://www.youtube.com/subscription_center?add_user=dnewschannel
DNews on Twitter http://twitter.com/dnews
Trace Dominguez on Twitter https://twitter.com/tracedominguez
Tara Long on Twitter https://twitter.com/TaraLongest
DNews on Facebook https://facebook.com/DiscoveryNews
DNews on Google+ http://gplus.to/dnews
Discovery News http://discoverynews.com
Download the TestTube App: http://testu.be/1ndmmMq
- published: 08 Nov 2014
- views: 76967
Space-Time And The Speed Of Light | Einstein's Relativity
http://facebook.com/ScienceReason ... Albert Einstein's Theory of Relativity (Chapter 3): Space-Time And The Speed Of Light
The concept of spacetime combines s...
http://facebook.com/ScienceReason ... Albert Einstein's Theory of Relativity (Chapter 3): Space-Time And The Speed Of Light
The concept of spacetime combines space and time to a single abstract "space", for which a unified coordinate system is chosen. Typically three spatial dimensions (length, width, height), and one temporal dimension (time) are required. Dimensions are independent components of a coordinate grid needed to locate a point in a certain defined "space"
---
Please subscribe to Science & Reason:
• http://www.youtube.com/Best0fScience
• http://www.youtube.com/ScienceMagazine
• http://www.youtube.com/ScienceTV
• http://www.youtube.com/FFreeThinker
---
SPACETIME
In physics, spacetime (or space-time) is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions. According to certain Euclidean space perceptions, the universe has three dimensions of space and one dimension of time. By combining space and time into a single manifold, physicists have significantly simplified a large number of physical theories, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels.
In classical mechanics, the use of Euclidean space instead of spacetime is appropriate, as time is treated as universal and constant, being independent of the state of motion of an observer. In relativistic contexts, however, time cannot be separated from the three dimensions of space, because the observed rate at which time passes for an object depends on the object's velocity relative to the observer and also on the strength of intense gravitational fields, which can slow the passage of time.
• http://en.wikipedia.org/wiki/Spacetime
---
GENERAL RELATIVITY
Special relativity is a theory of the structure of spacetime. It was introduced in Albert Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" (for the contributions of many other physicists see History of special relativity). Special relativity is based on two postulates which are contradictory in classical mechanics:
1. The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity),
2. The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.
The resultant theory agrees with experiment better than classical mechanics, e.g. in the Michelson-Morley experiment that supports postulate 2, but also has many surprising consequences. Some of these are:
* Relativity of simultaneity: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion.
* Time dilation: Moving clocks are measured to tick more slowly than an observer's "stationary" clock.
* Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer.
* Mass-energy equivalence: E = mc2, energy and mass are equivalent and transmutable.
* Maximum speed is finite: No physical object or message or field line can travel faster than light.
The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. (See Maxwell's equations of electromagnetism and introduction to special relativity).
• http://en.wikipedia.org/wiki/Theory_of_relativity
.
wn.com/Space Time And The Speed Of Light | Einstein's Relativity
http://facebook.com/ScienceReason ... Albert Einstein's Theory of Relativity (Chapter 3): Space-Time And The Speed Of Light
The concept of spacetime combines space and time to a single abstract "space", for which a unified coordinate system is chosen. Typically three spatial dimensions (length, width, height), and one temporal dimension (time) are required. Dimensions are independent components of a coordinate grid needed to locate a point in a certain defined "space"
---
Please subscribe to Science & Reason:
• http://www.youtube.com/Best0fScience
• http://www.youtube.com/ScienceMagazine
• http://www.youtube.com/ScienceTV
• http://www.youtube.com/FFreeThinker
---
SPACETIME
In physics, spacetime (or space-time) is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions. According to certain Euclidean space perceptions, the universe has three dimensions of space and one dimension of time. By combining space and time into a single manifold, physicists have significantly simplified a large number of physical theories, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels.
In classical mechanics, the use of Euclidean space instead of spacetime is appropriate, as time is treated as universal and constant, being independent of the state of motion of an observer. In relativistic contexts, however, time cannot be separated from the three dimensions of space, because the observed rate at which time passes for an object depends on the object's velocity relative to the observer and also on the strength of intense gravitational fields, which can slow the passage of time.
• http://en.wikipedia.org/wiki/Spacetime
---
GENERAL RELATIVITY
Special relativity is a theory of the structure of spacetime. It was introduced in Albert Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" (for the contributions of many other physicists see History of special relativity). Special relativity is based on two postulates which are contradictory in classical mechanics:
1. The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity),
2. The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.
The resultant theory agrees with experiment better than classical mechanics, e.g. in the Michelson-Morley experiment that supports postulate 2, but also has many surprising consequences. Some of these are:
* Relativity of simultaneity: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion.
* Time dilation: Moving clocks are measured to tick more slowly than an observer's "stationary" clock.
* Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer.
* Mass-energy equivalence: E = mc2, energy and mass are equivalent and transmutable.
* Maximum speed is finite: No physical object or message or field line can travel faster than light.
The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. (See Maxwell's equations of electromagnetism and introduction to special relativity).
• http://en.wikipedia.org/wiki/Theory_of_relativity
.
- published: 05 Aug 2010
- views: 1122328
Graphs of Planes in Three-Dimensional Space
The ways that planes can interact in three-dimensional space....
The ways that planes can interact in three-dimensional space.
wn.com/Graphs Of Planes In Three Dimensional Space
The ways that planes can interact in three-dimensional space.
Michio Kaku: The Multiverse Has 11 Dimensions
Don't miss new Big Think videos! Subscribe by clicking here: http://goo.gl/CPTsV5 The physicist explains why other universes in the mulitverse could have man......
Don't miss new Big Think videos! Subscribe by clicking here: http://goo.gl/CPTsV5 The physicist explains why other universes in the mulitverse could have man...
wn.com/Michio Kaku The Multiverse Has 11 Dimensions
Don't miss new Big Think videos! Subscribe by clicking here: http://goo.gl/CPTsV5 The physicist explains why other universes in the mulitverse could have man...
- published: 31 May 2011
- views: 659046
-
author: Big Think
WildLinAlg11: Applications of 3x3 matrices
This is the 11th lecture in this course on Linear Algebra by N J Wildberger. Here we talk about 3x3 matrices and their applications to linear transformations of...
This is the 11th lecture in this course on Linear Algebra by N J Wildberger. Here we talk about 3x3 matrices and their applications to linear transformations of three dimensional space. This includes dilations, reflections, rotations with plenty of examples.
CONTENT SUMMARY: pg 1: @00:08 matrix/vector multiplication; Two interpretations: linear transformation/Change of coordinates; active vs passive approach;
pg 2: @04:00 linear transformation approach; example; columns of transformation matrix are the 3 basis vectors transformed;
pg 3: @07:22 Identity transformation; dilations (scales the entire space); dilations are a closed system under composition and addition; remark on diagonal matrices and rational numbers;
pg 4: @11:09 mixed dilations; Mixed dilations are also a closed system under composition and addition;
pg 5: @14:15 examples; (easy) reflections; reflection in a plane; reflection in a line;
pg 6: @16:43 examples: (easy) projections; projection to a plane; projection to a line;
pg 7: @19:06 examples: (easy) rotations;
pg 8: @22:44 Rational rotations; half-turn formulation;
pg 9: @25:36 parallel projection of a vector (u) onto a plane at arbitrary projection direction (l);
pg 10: @29:10 The parallel projection matrix; projection properties;
pg 11: @31:15 projection example continued; projecting (u) onto the line (l); remark that the resulting matrix is rank 1;
pg 12: @35:48 A general reflection in a plane;
pg 13: @39:40 A general reflection in a line;
pg 14: @42:38 response of the general formulas in the case of perpendicular projection and reflection; introducing the notion of perpendicularity; the normal vector to a plane is read off as the coefficients of x,y,z in the cartesian formula of the plane;
pg 15: @46:26 revisit of the general formulas; the quadrance of the vector mentioned @48:20 ; remark on the benefits of abstraction @49:17 ;
pg 16 @51:11 exercises 11.(1:2) ; (THANKS to EmptySpaceEnterprise)
wn.com/Wildlinalg11 Applications Of 3X3 Matrices
This is the 11th lecture in this course on Linear Algebra by N J Wildberger. Here we talk about 3x3 matrices and their applications to linear transformations of three dimensional space. This includes dilations, reflections, rotations with plenty of examples.
CONTENT SUMMARY: pg 1: @00:08 matrix/vector multiplication; Two interpretations: linear transformation/Change of coordinates; active vs passive approach;
pg 2: @04:00 linear transformation approach; example; columns of transformation matrix are the 3 basis vectors transformed;
pg 3: @07:22 Identity transformation; dilations (scales the entire space); dilations are a closed system under composition and addition; remark on diagonal matrices and rational numbers;
pg 4: @11:09 mixed dilations; Mixed dilations are also a closed system under composition and addition;
pg 5: @14:15 examples; (easy) reflections; reflection in a plane; reflection in a line;
pg 6: @16:43 examples: (easy) projections; projection to a plane; projection to a line;
pg 7: @19:06 examples: (easy) rotations;
pg 8: @22:44 Rational rotations; half-turn formulation;
pg 9: @25:36 parallel projection of a vector (u) onto a plane at arbitrary projection direction (l);
pg 10: @29:10 The parallel projection matrix; projection properties;
pg 11: @31:15 projection example continued; projecting (u) onto the line (l); remark that the resulting matrix is rank 1;
pg 12: @35:48 A general reflection in a plane;
pg 13: @39:40 A general reflection in a line;
pg 14: @42:38 response of the general formulas in the case of perpendicular projection and reflection; introducing the notion of perpendicularity; the normal vector to a plane is read off as the coefficients of x,y,z in the cartesian formula of the plane;
pg 15: @46:26 revisit of the general formulas; the quadrance of the vector mentioned @48:20 ; remark on the benefits of abstraction @49:17 ;
pg 16 @51:11 exercises 11.(1:2) ; (THANKS to EmptySpaceEnterprise)
- published: 09 Mar 2011
- views: 3553
Vectors in Three Dimensional Space - Section 8.3
This Precalculus lesson is very similar to what we did with two dimension vectors (section 8.2). Magnitude and unit vectors are included....
This Precalculus lesson is very similar to what we did with two dimension vectors (section 8.2). Magnitude and unit vectors are included.
wn.com/Vectors In Three Dimensional Space Section 8.3
This Precalculus lesson is very similar to what we did with two dimension vectors (section 8.2). Magnitude and unit vectors are included.
- published: 25 Mar 2014
- views: 7
WildLinAlg9a: Three dimensional affine geometry
This is the first video of the ninth lecture of this course on Linear Algebra. Here we give a gentle introduction to three dimensional space, starting with t......
This is the first video of the ninth lecture of this course on Linear Algebra. Here we give a gentle introduction to three dimensional space, starting with t...
wn.com/Wildlinalg9A Three Dimensional Affine Geometry
This is the first video of the ninth lecture of this course on Linear Algebra. Here we give a gentle introduction to three dimensional space, starting with t...
Asiro - Three-dimensional space
Asiro - Nocturnal Asiro - Physical p l a n e Asiro - microwave beat --- https://soundcloud.com/asiroerudite http://asiroerudite.bandcamp.com/...
Asiro - Nocturnal Asiro - Physical p l a n e Asiro - microwave beat --- https://soundcloud.com/asiroerudite http://asiroerudite.bandcamp.com/
wn.com/Asiro Three Dimensional Space
Asiro - Nocturnal Asiro - Physical p l a n e Asiro - microwave beat --- https://soundcloud.com/asiroerudite http://asiroerudite.bandcamp.com/
- published: 11 Jun 2013
- views: 116
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author: psyhost
[Multivariable Calculus] Points and Vectors in Three Dimensional Space
In this video I go over one, two, and three dimensional space and points in those spaces. Then I quickly review the basics of vectors, including magnitude, vect...
In this video I go over one, two, and three dimensional space and points in those spaces. Then I quickly review the basics of vectors, including magnitude, vector addition and subtraction, scalar multiplication, and unit vectors. I also show how a point can be represented by its corresponding position vector in standard position. Lastly, I go over the standard basis vectors in three dimensional space.
If you have any questions, feedback, or video requests, please leave a comment.
wn.com/Multivariable Calculus Points And Vectors In Three Dimensional Space
In this video I go over one, two, and three dimensional space and points in those spaces. Then I quickly review the basics of vectors, including magnitude, vector addition and subtraction, scalar multiplication, and unit vectors. I also show how a point can be represented by its corresponding position vector in standard position. Lastly, I go over the standard basis vectors in three dimensional space.
If you have any questions, feedback, or video requests, please leave a comment.
- published: 26 Aug 2015
- views: 22
Hidden Dimensions: Exploring Hyperspace
Extra dimensions of space—the idea that we are immersed in hyperspace—may be key to explaining the fundamental nature of the universe. Relativity introduced tim...
Extra dimensions of space—the idea that we are immersed in hyperspace—may be key to explaining the fundamental nature of the universe. Relativity introduced time as the fourth dimension, and Einstein’s subsequent work envisioned more dimensions still--but ultimately hit a dead end. Modern research has advanced the subject in ways he couldn’t have imagined. John Hockenberry joins Brian Greene, Lawrence Krauss, and other leading thinkers on a visual tour through wondrous spatial realms that may lie beyond the ones we experience.
Sign up for our free newsletter to see exclusive features and be the first to get news and updates on upcoming WSF programs: http://www.worldsciencefestival.com/newsletter-youtube/
wn.com/Hidden Dimensions Exploring Hyperspace
Extra dimensions of space—the idea that we are immersed in hyperspace—may be key to explaining the fundamental nature of the universe. Relativity introduced time as the fourth dimension, and Einstein’s subsequent work envisioned more dimensions still--but ultimately hit a dead end. Modern research has advanced the subject in ways he couldn’t have imagined. John Hockenberry joins Brian Greene, Lawrence Krauss, and other leading thinkers on a visual tour through wondrous spatial realms that may lie beyond the ones we experience.
Sign up for our free newsletter to see exclusive features and be the first to get news and updates on upcoming WSF programs: http://www.worldsciencefestival.com/newsletter-youtube/
- published: 15 Jan 2015
- views: 42282
[Multivariable Calculus] Equations of Lines in Three Dimensional Space
In this video I show how to represent a line in three dimensional space with its vector equation by finding an initial point and direction vector. I also show h...
In this video I show how to represent a line in three dimensional space with its vector equation by finding an initial point and direction vector. I also show how to represent a line with its parametric equations and symmetric equations, and go over a quick example illustrating these points.
If you have any questions, feedback, or video requests, please leave a comment.
wn.com/Multivariable Calculus Equations Of Lines In Three Dimensional Space
In this video I show how to represent a line in three dimensional space with its vector equation by finding an initial point and direction vector. I also show how to represent a line with its parametric equations and symmetric equations, and go over a quick example illustrating these points.
If you have any questions, feedback, or video requests, please leave a comment.
- published: 27 Aug 2015
- views: 1
WildLinAlg9: Three dimensional affine geometry
This is the ninth lecture of this course on Linear Algebra by N J Wildberger. Here we give a gentle introduction to three dimensional space, starting with th......
This is the ninth lecture of this course on Linear Algebra by N J Wildberger. Here we give a gentle introduction to three dimensional space, starting with th...
wn.com/Wildlinalg9 Three Dimensional Affine Geometry
This is the ninth lecture of this course on Linear Algebra by N J Wildberger. Here we give a gentle introduction to three dimensional space, starting with th...