Euclidean geometry | Pythagorean theorem | Theorems about quadrilaterals
In Euclidean geometry, the British flag theorem says that if a point P is chosen inside a rectangle ABCD then the sum of the squares of the Euclidean distances from P to two opposite corners of the rectangle equals the sum to the other two opposite corners.As an equation: The theorem also applies to points outside the rectangle, and more generally to the distances from a point in Euclidean space to the corners of a rectangle embedded into the space. Even more generally, if the sums of squares of distances from a point P to the two pairs of opposite corners of a parallelogram are compared, the two sums will not in general be equal, but the difference of the two sums will depend only on the shape of the parallelogram and not on the choice of P. The theorem can also be thought of as a generalisation of the Pythagorean theorem. Placing the point P on any of the four vertices of the rectangle yields the square of the diagonal of the rectangle being equal to the sum of the squares of the width and length of the rectangle, which is the Pythagorean theorem. (Wikipedia).
What is the ham sandwich theorem?
From playlist Mathematics
Proof: The Angle Bisector Theorem
This video states and proves the angle bisector theorem. Complete Video List: http://www.mathispower4u.yolasite.com
From playlist Relationships with Triangles
What is Stokes theorem? - Formula and examples
â–º My Vectors course: https://www.kristakingmath.com/vectors-course Where Green's theorem is a two-dimensional theorem that relates a line integral to the region it surrounds, Stokes theorem is a three-dimensional version relating a line integral to the surface it surrounds. For that reaso
From playlist Vectors
This video states and investigates the triangle inequality theorem. Complete Video List: http://www.mathispower4u.yolasite.com
From playlist Relationships with Triangles
In this video, I present another example of Stokes theorem, this time using it to calculate the line integral of a vector field. It is a very useful theorem that arises a lot in physics, for example in Maxwell's equations. Other Stokes Example: https://youtu.be/-fYbBSiqvUw Yet another Sto
From playlist Vector Calculus
The Goldman symplectic form on the Hitchin component by Tengren Zhang
SURFACE GROUP REPRESENTATIONS AND GEOMETRIC STRUCTURES DATE: 27 November 2017 to 30 November 2017 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classi
From playlist Surface Group Representations and Geometric Structures
How To Solve Microsoft's Rectangle Corners Interview Question
ABCD is a rectangle. Point P is 11 units from A, 13 units from B, and 7 units from C. What is the distance from P to D? Note: the point P could be inside or outside the rectangle. A version of this problem has been asked as a Microsoft interview question. Can you figure it out? Watch the v
From playlist Math Puzzles, Riddles And Brain Teasers
What is the SAS Congruence Theorem for Triangles - Congruent Triangles
👉 Learn about congruent triangles theorems. Two or more triangles (or polygons) are said to be congruent if they have the same shape and size. There are many methods to determine whether two triangles are congruent. Some of the methods include: (1) The SSS (Side Side Side) congruency the
From playlist Congruent Triangles
Proof: The Isosceles Triangle Theorem
Complete videos list: http://mathispower4u.yolasite.com/ This video provides a two column proof of the isosceles triangle theorem.
From playlist Triangles and Congruence
What is the Definition of Congruent Triangles - Congruent Triangles
👉 Learn about congruent triangles theorems. Two or more triangles (or polygons) are said to be congruent if they have the same shape and size. There are many methods to determine whether two triangles are congruent. Some of the methods include: (1) The SSS (Side Side Side) congruency the
From playlist Congruent Triangles
Using the properties of rectangles to solve for x
👉 Learn how to solve problems with rectangles. A rectangle is a parallelogram with each of the angles a right angle. Some of the properties of rectangles are: each pair of opposite sides are equal, each pair of opposite sides are parallel, all the angles are right angles, the diagonals are
From playlist Properties of Rectangles
Follow-Up: Finite Difference Method
Original Video here: https://youtu.be/scQ51q_1nhw Videos mentioned: James Tanton https://youtu.be/_5vU48kf7NY Mathologer https://youtu.be/4AuV93LOPcE More on Gilbreath's conjecture here: https://primes.utm.edu/glossary/page.php?sort=GilbreathsConjecture Here is finite differences on wik
From playlist My Maths Videos
R. Ghezzi - Volume measures in non equiregular sub-Riemannian manifolds
In this talk we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it to a smooth volume. First we give the Lebesgue decomposition of the Hausdorff volume. Then we focus on the regular part, show that it is not commensurable with a smooth volume and give
From playlist Journées Sous-Riemanniennes 2017
Funeral Of Kemal Atatürk: Former President of Turkey (1938) | British Pathé
This silent footage from 1938 shows the funeral of former President Mustafa Kemal Atatürk of Turkey along with numerous soldiers and dignitaries marching with the coffin in tribute. For Archive Licensing Enquiries Visit: https://goo.gl/W4hZBv Explore Our Online Channel For FULL Documenta
From playlist British Pathé | Explore the Archive
NIPS 2017 Human-Computer Question Answering Competition: 2nd Place Team vs. UMD
The 2nd place computer team takes on the UMD quiz bowl team. Chronologically, this happened after the NIPS competition on Long Beach. No powers in this match, and although the screen says "OUSIA", the answers are indeed from the "Etherial" team. For more information: https://sites.googl
From playlist Human-Computer QA
Yanks Enter Tokyo: U.S. Soldiers in Japan (1945) | British Pathé
This Pathé newsreel covers the arrival of the U.S. army in Tokyo, Japan in 1945 after the Allies won World War II. For Archive Licensing Enquiries Visit: https://goo.gl/W4hZBv Explore Our Online Channel For FULL Documentaries, Fascinating Interviews & Classic Movies: https://goo.gl/7dVe8
From playlist British Pathé | Explore the Archive
"A Brief but Furious Campaign": The Battle of the Pearl River Forts
The November 1856 Battle of the Barrier Forts, while a testimony to the prowess of the U.S. Navy and Marine Corps, is perhaps one of the most obscure applications of U.S. military force in history. The History Guy remembers "A Brief but Furious Campaign". This is original content based on
From playlist China and the Far East
Robert Kennedy Funeral (1968) | British Pathé
Witness the tragic footage of former U.S. Senator Robert Kennedy's funeral that took place in New York and Washington D.C. in 1968. A variety of politicians were in attendance including President Lyndon B. Johnson and his eventual successor President Richard Nixon. For Archive Licensing
From playlist British Pathé | Explore the Archive
First Opium War - Gunboat Diplomacy - Extra History - #3
The British set up a blockade outside Canton, but one of their own private merchant ships tried to run through it. When the Chinese came to its defense, war began in earnest. Since the British had far superior firepower, they easily conquered Chuenpee and Chusan. Elliot and the Emperor's n
From playlist Extra History: Chronological Order (1700 CE - Present)
Determining the Unit Tangent Vector
This video explains how to determine the unit tangent vector to a curve defined by a vector valued function. http://mathispower4u.wordpress.com/
From playlist Vectors