Affine geometry | Articles containing proofs | Theorems about triangles | Euclidean plane geometry
Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ABC, and a transversal line that crosses BC, AC, and AB at points D, E, and F respectively, with D, E, and F distinct from A, B, and C. A weak version of the theorem states that where |AB| is taken to be the ordinary length of segment AB: a positive value. The theorem can be strengthened to a statement about signed lengths of segments, which provides some additional information about the relative order of collinear points. Here, the length AB is taken to be positive or negative according to whether A is to the left or right of B in some fixed orientation of the line; for example, AF/FB is defined as having positive value when F is between A and B and negative otherwise. The signed version of Menelaus's theorem states Equivalently, Some authors organize the factors differently and obtain the seemingly different relation but as each of these factors is the negative of the corresponding factor above, the relation is seen to be the same. The converse is also true: If points D, E, and F are chosen on BC, AC, and AB respectively so that then D, E, and F are collinear. The converse is often included as part of the theorem. (Note that the converse of the weaker, unsigned statement is not necessarily true.) The theorem is very similar to Ceva's theorem in that their equations differ only in sign. By re-writing each in terms of cross-ratios, the two theorems may be seen as projective duals. (Wikipedia).
C73 Introducing the theorem of Frobenius
The theorem of Frobenius allows us to calculate a solution around a regular singular point.
From playlist Differential Equations
Solve a Bernoulli Differential Equation Initial Value Problem
This video provides an example of how to solve an Bernoulli Differential Equations Initial Value Problem. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
Menelaus, Ceva and the laws of proportion | Universal Hyperbolic Geometry 31 | NJ Wildberger
The classical theorems of Menelaus and Ceva concern a triangle together with an additional line or point, and give relations between three ratios of distances (or quadrances). These results are also valid in universal hyperbolic geometry. However we also give some other lovely and simple r
From playlist Universal Hyperbolic Geometry
Novel Algebraic Operations for Affine Geometry | Algebraic Calculus One | Wild Egg
We introduce some novel conventions to help us set up the foundations of affine geometry. We learn about differences of points, sums of points and vectors, affine combinations and vector proportions. And then use these to state a number of important results from affine geometry, including
From playlist Algebraic Calculus One from Wild Egg
Spherical and elliptic geometries (cont.) | Universal Hyperbolic Geometry 34 | NJ Wildberger
We continue our introduction to spherical and elliptic geometries, starting with a discussion of longitude and latitude on a sphere. We mention the close historical connections between spherical geometry and astronomy, going back to the ancient Greeks, to the Indians and to the Arabs. We
From playlist Universal Hyperbolic Geometry
How Greek Maths Changed the World - with Alan Davies
Professor Alan Davies presents a series of groundbreaking experiments pioneered by the Ancient Greeks. Often called the "birthplace of civilisation", Ancient Greece heralded numerous advances in philosophy, science, engineering and mathematics which have shaped our understanding of the mod
From playlist Mathematics
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
Solve a Bernoulli Differential Equation (Part 1)
This video provides an example of how to solve an Bernoulli Differential Equation. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
The Iliad - Deadly Destiny - Extra Mythology - #3
Watch Extra Mythology ad-free on Nebula! https://go.nebula.tv/extramythology Gods and goddesses join the fray and continue to drive the tides of war. Paris tries to end the bloody battle in a single one on one fight but it isn't meant to be. Ares and Aphrodite side with the Trojans, Hera
From playlist Extra Mythology (ALL EPISODES)
Solve a Bernoulli Differential Equation (Part 2)
This video provides an example of how to solve an Bernoulli Differential Equation. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
Proof of Bernoulli's Inequality using Mathematical Induction
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Bernoulli's Inequality using Mathematical Induction
From playlist Proofs
11. John Barth, Lost in the Funhouse
The American Novel Since 1945 (ENGL 291) In her lecture on John Barth's collection of stories Lost in the Funhouse, Professor Amy Hungerford delves beyond the superficial pleasures and frustrations of Barth's oft-cited metafictional masterwork to illuminate the profound commitment to la
From playlist The American Novel Since 1945 with Amy Hungerford
The Iliad - Prelude to War - Extra Mythology - #1
Watch Extra Mythology ad-free on Nebula! https://go.nebula.tv/extramythology Ah, the myth that launched a thousand ships. The apple thrown into the middle of a greek banquet would ruin lives and lay waste to entire kingdoms. We set the stage for Helen and Paris, two lovers who were not me
From playlist Extra Mythology (ALL EPISODES)
Laws of Proportion for a Triangle | WildTrig: Intro to Rational Trigonometry | N J Wildberger
Using rational trigonometry we develop Menelaus' and Ceva's theorem and some related results, namely the Law of Proportions, and the Alternating spreads theorem. ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concis
From playlist WildTrig: Intro to Rational Trigonometry
This is a (stand-alone) continuation of the previous video at: https://youtu.be/2vnqSwWAn34 Featuring Tadashi Tokieda. More links & stuff in full description below ↓↓↓ More Tadashi: http://bit.ly/tadashi_vids Playing cards latest: http://www.bradyharanblog.com/numberphile-playing-cards
From playlist Tadashi Tokieda on Numberphile
Ex: Solve a Bernoulli Differential Equation Using an Integrating Factor
This video explains how to solve a Bernoulli differential equation. http://mathispower4u.com
From playlist Bernoulli Differential Equations
Which Bible Characters are Historical?
Buy the poster: https://usefulcharts.com/products/biblical-family-tree BIBLICAL GENEALOGY SERIES: ========================= Episode 1: Which Bible Characters are Historical? https://youtu.be/aLtRR9RgFMg Episode 2: Adam to David https://youtu.be/I6Oj-HyHIAY Episode 3:- Kings of Israel
From playlist Religious Studies