Circles defined for a triangle
In geometry, the orthocentroidal circle of a non-equilateral triangle is the circle that has the triangle's orthocenter and centroid at opposite ends of its diameter. This diameter also contains the triangle's nine-point center and is a subset of the Euler line, which also contains the circumcenter outside the orthocentroidal circle. Andrew Guinand showed in 1984 that the triangle's incenter must lie in the interior of the orthocentroidal circle, but not coinciding with the nine-point center; that is, it must fall in the open orthocentroidal disk punctured at the nine-point center. The incenter could be any such point, depending on the specific triangle having that particular orthocentroidal disk. Furthermore, the Fermat point, the Gergonne point, and the symmedian point are in the open orthocentroidal disk punctured at its own center (and could be at any point therein), while the second Fermat point and Feuerbach point are in the exterior of the orthocentroidal circle. The set of potential locations of one or the other of the Brocard points is also the open orthocentroidal disk. The square of the diameter of the orthocentroidal circle is where a, b, and c are the triangle's side lengths and D is the diameter of its circumcircle. (Wikipedia).
Orthocenters exist! | Universal Hyperbolic Geometry 10 | NJ Wildberger
In classical hyperbolic geometry, orthocenters of triangles do not in general exist. Here in universal hyperbolic geometry, they do. This is a crucial building block for triangle geometry in this subject. The dual of an orthocenter is called an ortholine---also not seen in classical hyperb
From playlist Universal Hyperbolic Geometry
How to find the point on the unit circle from the given real number
š 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)
Quickly fill in the unit circle by understanding reference angles and quadrants
š 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 find the point of the unit circle when given a specific angle
š 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)
Orthogonality and Orthonormality
We know that the word orthogonal is kind of like the word perpendicular. It implies that two vectors have an angle of ninety degrees or half pi radians between them. But this term means much more than this, as we can have orthogonal matrices, or entire subspaces that are orthogonal to one
From playlist Mathematics (All Of It)
How to determine the point on the unit circle given an angle
š 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 point on the unit circle given an angle
š 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)
Determine the point on the unit circle for an angle
š 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)
Determining where a point is on the unit circle
š 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)
The man who loved circles (Objectivity): https://youtu.be/AzmUCL1OHhs More links & stuff in full description below āāā Pappus chains, circle inversion and a whole lot more in this EPIC video with Simon Pampena. Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Websit
From playlist Numberphile Videos
Steiner's Porism: proving a cool animation #SoME1
Strange circle stuff. (Some people have commented that the audio is really low. Unfortunately I haven't found a way to fix it without re-uploading the whole video, but your feedback will be taken on board for the next video! Also to everyone begging for more content, Iām currently in the m
From playlist Summer of Math Exposition Youtube Videos
Coding Challenge #50.1: Animated Circle Packing - Part 1
In this multi-part coding challenge, I demonstrate how to use a circle packing algorithm. Code: https://thecodingtrain.com/challenges/50-animated-circle-packing p5.js Web Editor Sketches: š¹ļø Animated Circle Packing - Text: https://editor.p5js.org/codingtrain/sketches/wxGRAd4I- š¹ļø Animated
From playlist Coding Challenges
9.8: Random Circles with No Overlap - p5.js Tutorial
This video demonstrates a "circle packing"-like algorithm. Circles are placed randomly in the canvas, but only if they are not overlapping with any previous circles. This is referred to as "uniform random sampling." The p5.js dist() function is demonstrated. Source-code: https://github.
From playlist 9: Additional Topics - p5.js Tutorial
Circles (Complete Geometry Course Lesson 10)
This is the tenth lesson in the Mario's Math Tutoring's Complete Geometry Course here on YouTube! In this video we take a deep dive into circles discussing formulas related to central angles, inscribed angles, arc measures, chord lengths, secant lengths, tangent lengths, and more! Join th
From playlist Geometry Course (Complete Course - Mario's Math Tutoring)
How to Draw Tangent Circles using Cones
Solving the Problem of Apollonius with Conic Sections This video describes a non-standard way of finding tangent circles to a given set of 3 circles, known as the Problem of Apollonius. It uses conic sections rather than straightedge and compass. I feel this approach is more intuitive and
From playlist Summer of Math Exposition Youtube Videos
What is a power of a point? or a radical axis? and how are they useful?
Here we explain what is a power of a point, a radical axis and a radical center and we show a problem where we use all three to get to the solution and yes, this is my SoME2 submission. Please subscribe: https://www.youtube.com/channel/UCs9k80C32DtCNMBC5aMoHkQ
From playlist Summer of Math Exposition 2 videos
This geometry video tutorial provides a basic introduction into circle theorems. It contains plenty of examples and practice problems. Here is a list of topics: 1. If a radius is perpendicular to a chord, it bisects the chord into two congruent segments. The point of contact is the mid
From playlist Geometry Video Playlist
š 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)
Coding Math: Episode 53 - Random Circle Packing
A quick, fun video on a technique known as circle packing. Or at least one take on the technique. Support Coding Math: http://patreon.com/codingmath Source Code: http://github.com/bit101/codingmath Source for this episode: http://jsbin.com/fegeti/edit?js,output Mario: https://www.flickr.
From playlist Episodes