Circles | Spherical curves | Elementary geometry | Spherical trigonometry | Riemannian geometry
In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry are the natural analog of straight lines in Euclidean space. For any pair of distinct non-antipodal points on the sphere, there is a unique great circle passing through both. (Every great circle through any point also passes through its antipodal point, so there are infinitely many great circles through two antipodal points.) The shorter of the two great-circle arcs between two distinct points on the sphere is called the minor arc, and is the shortest surface-path between them. Its arc length is the great-circle distance between the points (the intrinsic distance on a sphere), and is proportional to the measure of the central angle formed by the two points and the center of the sphere. A great circle is the largest circle that can be drawn on any given sphere. Any diameter of any great circle coincides with a diameter of the sphere, and therefore every great circle is concentric with the sphere and shares the same radius. Any other circle of the sphere is called a small circle, and is the intersection of the sphere with a plane not passing through its center. Small circles are the spherical-geometry analog of circles in Euclidean space. Every circle in Euclidean 3-space is a great circle of exactly one sphere. The disk bounded by a great circle is called a great disk: it is the intersection of a ball and a plane passing through its center.In higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space Rn + 1. (Wikipedia).
The Circle (1 of 2: Starting with a verbal definition)
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From playlist Functions & Other Graphs
From playlist Miscellaneous
What exactly is a circle? | Arithmetic and Geometry Math Foundations 28 | N J Wildberger
Moving beyond points and lines, circles are the next geometrical objects we encounter. Here we address the question of how best to introduce this important notion, strictly in the setting of rational numbers, and without metaphysical waffling about `infinite sets.' This lecture is part of
From playlist Math Foundations
The unit circle plays a key role in understanding how circles and triangles are connected, as well as providing a simple way to introduce the basic trigonometric functions (sine, cosine and tangent). This video describes the unit circle very carefully with the goals of providing basic insi
From playlist Trigonometry
Circles: Radius, Diameter, Chords, Circumference, and Sectors
Is there anything more aesthetically pleasing than a perfect circle? It may seem like the king of shapes, but it's also arguably the simplest. Define a central point and a radius, and you've got a circle. What else can we say about circles? Let's find out! Watch the whole Mathematics play
From playlist Geometry
What is a central angle of a circle
Learn the essential definitions of the parts of a circle. A secant line to a circle is a line that crosses exactly two points on the circle while a tangent line to a circle is a line that touches exactly one point on the circle. A chord is a line that has its two endpoints on the circle.
From playlist Essential Definitions for Circles #Circles
What is the definition of a tangent line to a circle
Learn the essential definitions of the parts of a circle. A secant line to a circle is a line that crosses exactly two points on the circle while a tangent line to a circle is a line that touches exactly one point on the circle. A chord is a line that has its two endpoints on the circle.
From playlist Essential Definitions for Circles #Circles
Earth Geometry lesson 2 - Distance between two points on great circle
In this lesson we talk about how to find the distance between two points on the same great circle (i.e. same longitude, or two points on the equator).
From playlist Maths A / General Course, Grade 11/12, High School, Queensland, Australia
Geometry of the Earth (1 of 3: Basic shapes & ideas)
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From playlist Working with Time
Area of a Sector, Angular Velocity, Applications (Precalculus - Trigonometry 5)
How to find the Area of a Sector, Arc Length on a great circle of a sphere, Angular Velocity, Rotational Velocity, and other applications. Support: https://www.patreon.com/ProfessorLeonard
From playlist Precalculus - College Algebra/Trigonometry
[#SoME1] A simple statement with a remarkable proof ( + Proof of Bolzano-Weierstrass Theorem)
In this video, I present a very important statement that, at first, seems quite obvious, but whose proof requires some neat reasoning. I start off by explaining everything required in order to understand the problem, and then restate it in a more rigorous way. Then, I present two proofs f
From playlist Summer of Math Exposition Youtube Videos
Geometry of the Earth (2 of 3: Example conceptual questions)
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From playlist Working with Time
Equation of a Circle of Latitude
Have you ever wanted to know the equation of a circle of latitude? Take a look.
From playlist Summer of Math Exposition Youtube Videos
Geometry - Geodesics: Oxford Mathematics 1st Year Student Lecture
This is the third lecture we are showing from Derek Moulton's first-year Geometry course. In this video, Derek discuss the idea of the shortest path between two points on a surface. Such paths follow a curve known as a geodesic. He works through some basic calculations and aims to build in
From playlist Oxford Mathematics 1st Year Student Lectures
MIT 3.60 | Lec 7b: Symmetry, Structure, Tensor Properties of Materials
Part 2: 2D Plane Groups, Lattices (cont.) View the complete course at: http://ocw.mit.edu/3-60F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
👉 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)
Learn how to determine the volume of a sphere
👉 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