In mathematics, a unit sphere is simply a sphere of radius one around a given center. More generally, it is the set of points of distance 1 from a fixed central point, where different norms can be used as general notions of "distance". A unit ball is the closed set of points of distance less than or equal to 1 from a fixed central point. Usually the center is at the origin of the space, so one speaks of "the unit ball" or "the unit sphere".Special cases are the unit circle and the unit disk. The importance of the unit sphere is that any sphere can be transformed to a unit sphere by a combination of translation and scaling. In this way the properties of spheres in general can be reduced to the study of the unit sphere. (Wikipedia).
Quickly fill in the unit circle by understanding reference angles and quadrants
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Trigonometric Functions and The Unit Circle
Learn how to construct the unit circle
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
How to memorize the unit circle
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
Watch me complete the unit circle
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
How to quickly write out the unit circle
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
Why the unit circle is so helpful for us to evaluate trig functions
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Trigonometric Functions and The Unit Circle
Learn how to determine the volume of a sphere
π Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
Thinking outside the 10-dimensional box
Visualizing high-dimensional spheres to understand a surprising puzzle. Help fund future projects: https://www.patreon.com/3blue1brown This video was sponsored by Brilliant: https://brilliant.org/3b1b An equally valuable form of support is to simply share some of the videos. Special thanks
From playlist Neat proofs/perspectives
Finding the volume and the surface area of a sphere
π Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
Lecture 5 of Leonard Susskind's Modern Physics concentrating on Cosmology. Recorded February 16, 2009 at Stanford University. This Stanford Continuing Studies course is the fifth of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The
From playlist Lecture Collection | Modern Physics: Cosmology
(January 28, 2013) Leonard Susskind presents three possible geometries of homogeneous space: flat, spherical, and hyperbolic, and develops the metric for these spatial geometries in spherical coordinates. Originally presented in the Stanford Continuing Studies Program. Stanford Universit
From playlist Lecture Collection | Cosmology
Visualizing quaternions (4d numbers) with stereographic projection
How to think about this 4d number system in our 3d space. Part 2: https://youtu.be/zjMuIxRvygQ Interactive version of these visuals: https://eater.net/quaternions Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of t
From playlist Explainers
Suppose that a function u equals to its average value on every ball and every sphere, what can we say about u? It turns out that u has to solve Laplaceβs equation! Conversely, if u solves Laplaceβs equation, then u must satisfy the above mean-value property. In this video, I state and pro
From playlist Partial Differential Equations
Lecture 23: Gaussian Image, Solids of Revolution, Direction Histograms, Regular Polyhedra
MIT 6.801 Machine Vision, Fall 2020 Instructor: Berthold Horn View the complete course: https://ocw.mit.edu/6-801F20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63pfpS1gV5P9tDxxL_e4W8O In this lecture, we cover more on the Gaussian images and extended Gaussian image
From playlist MIT 6.801 Machine Vision, Fall 2020
Lecture 15: Radiometry (CMU 15-462/662)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/
From playlist Computer Graphics (CMU 15-462/662)
Probability With Geometry - Length, Area & Volume
This geometry video tutorial provides a basic introduction into probability. It's a nice review that explains how to calculate the probability given the length of a segment, the area of triangles and rectangles or the volume of a sphere within a cube. This video contains plenty of exampl
From playlist Geometry Video Playlist
Michael Farber (2/24/22): Topological complexity of spherical bundles
I will start by describing the concept of a parametrized motion planning algorithm which allows to achieve high degree of flexibility and universality. The main part of the talk will focus on the problem of understanding the parametrized topological complexity of sphere bundles. I will exp
From playlist Topological Complexity Seminar
How to determine the point on the unit circle given an angle
π Learn how to find the point on the unit circle given the angle of the point. A unit circle is a circle whose radius is 1. Given an angle in radians, to find the coordinate of points on the unit circle made by the given angle with the x-axis at the center of the unit circle, we plot the a
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
How to Find a Random Point in a High Dimensional Ball #SoME2
My video for the SoME2 competition hosted by 3Blue1Brown. References: - Justin's video: "The BEST Way to Find a Random Point in a Circle" (https://www.youtube.com/watch?v=4y_nmpv-9lI&list=PLnQX-jgAF5pTkwtUuVpqS5tuWmJ-6ZM-Z&index=6&t=3s) - "Vector Calculus, Linear Algebra, and Differential
From playlist Summer of Math Exposition 2 videos