Articles containing proofs | Theorems in projective geometry | Euclidean plane geometry
In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that * given one set of collinear points and another set of collinear points then the intersection points of line pairs and and and are collinear, lying on the Pappus line. These three points are the points of intersection of the "opposite" sides of the hexagon . It holds in a projective plane over any field, but fails for projective planes over any noncommutative division ring. Projective planes in which the "theorem" is valid are called pappian planes. If one restricts the projective plane such that the Pappus line is the line at infinity, one gets the affine version of Pappus's theorem shown in the second diagram. If the Pappus line and the lines have a point in common, one gets the so-called little version of Pappus's theorem. The dual of this incidence theorem states that given one set of concurrent lines , and another set of concurrent lines , then the lines defined by pairs of points resulting from pairs of intersections and and and are concurrent. (Concurrent means that the lines pass through one point.) Pappus's theorem is a special case of Pascal's theorem for a conic—the limiting case when the conic degenerates into 2 straight lines. Pascal's theorem is in turn a special case of the Cayley–Bacharach theorem. The Pappus configuration is the configuration of 9 lines and 9 points that occurs in Pappus's theorem, with each line meeting 3 of the points and each point meeting 3 lines. In general, the Pappus line does not pass through the point of intersection of and . This configuration is self dual. Since, in particular, the lines have the properties of the lines of the dual theorem, and collinearity of is equivalent to concurrence of , the dual theorem is therefore just the same as the theorem itself. The Levi graph of the Pappus configuration is the Pappus graph, a bipartite distance-regular graph with 18 vertices and 27 edges. (Wikipedia).
Pythagorean Theorem III (visual proof)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the semicircle and Thales triangle theorem. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. #mathshorts #m
From playlist Pythagorean Theorem
Pythagorean Theorem II (visual proof)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using a dissection of a square in two different ways. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. #mathshort
From playlist Pythagorean Theorem
Pythagorean Theorem V (visual proof; Leonardo da Vinci)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the a diagram that is now attributed to Leonardo da Vinci. The proof uses reflection and rotation symmetry arguments. This theorem states the square of the hypotenuse of a right triangle is
From playlist Pythagorean Theorem
Pythagorean Theorem I (visual proof)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the hypotenuses of scaled triangles. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. #mathshorts #mathvide
From playlist Pythagorean Theorem
Applying the pythagorean formula to multiple triangles to find the missing length
Learn about the Pythagorean theorem. The Pythagoras theorem is a fundamental relation among the three sides of a right triangle. It is used to determine the missing length of a right triangle. The Pythagoras theorem states that the square of the hypotenuse (the side opposite the right angl
From playlist Geometry - PYTHAGOREAN THEOREM
algebraic geometry 3 Bezout, Pappus, Pascal
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives more examples and applications of algebraic geometry, including Bezout's theorem, Pauppus's theorem, and Pascal's theorem.
From playlist Algebraic geometry I: Varieties
When a genius 16 year old Pascal discovered a geometry pattern
Pascal discovered this amazing geometry result when he was only 16. The book "The Art of the Infinite" by Robert Kaplan and Ellen Kaplan has a wonderful introduction to projective geometry and a proof this this theorem. Proof of Pascal's Theorem for the Circle (which also proves any conic
From playlist Mental Math Tricks
Theorem of Pappus to find Volume of Revolution Calculus 2
If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage www.YouTube.com/Profrobbob I introduce the Theorem of Pappus and then work through 2 examples. The first example is finding the volume of a Tarus at 2:40 and the second ex
From playlist Calculus 2
What is the formula for the pythagorean theorem
Learn about the Pythagorean theorem. The Pythagoras theorem is a fundamental relation among the three sides of a right triangle. It is used to determine the missing length of a right triangle. The Pythagoras theorem states that the square of the hypotenuse (the side opposite the right angl
From playlist Geometry - PYTHAGOREAN THEOREM
Visual Proof of Pythagoras' Theorem
More resources available at www.misterwootube.com
From playlist Pythagoras’ Theorem
Mechanical Engineering: Centroids & Center of Gravity (25 of 35) Pappus-Guldinus Theorem 2 Explained
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the first theorem of Pappus-Guldinius of finding the volume of an object. Next video in this series can be seen at: https://youtu.be/Ca-hf-1RtY8
From playlist MECHANICAL ENGINEERING 4 - CENTER OF GRAVITY
Mechanical Engineering: Centroids & Center of Gravity (30 of 35) Area, Vol=? using Pappus-Guldinus
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the area and volume of a ½ circle rotated about the x-axis. Next video in this series can be seen at: https://youtu.be/fDJWSK-wWtk
From playlist MECHANICAL ENGINEERING 4 - CENTER OF GRAVITY
Pythagorean Theorem VI (visual proof; Euclid's proof; 4K)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) following essentially Euclid's proof. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. #math #pythagoreantheorem
From playlist Pythagorean Theorem
Geometrical Snapshots from Ancient Times to Modern Times - Tom M. Apostol - 11/5/2013
The 23rd Annual Charles R. DePrima Memorial Undergraduate Mathematics Lecture by Professor Tom M. Apostol was presented on November 5, 2013, in Baxter Lecture Hall at Caltech in Pasadena, CA, USA. For more info, visit http://math.caltech.edu/events/14deprima.html Produced in association w
From playlist Research & Science
How to apply the pythagorean theorem to a triangle
Learn about the Pythagorean theorem. The Pythagoras theorem is a fundamental relation among the three sides of a right triangle. It is used to determine the missing length of a right triangle. The Pythagoras theorem states that the square of the hypotenuse (the side opposite the right angl
From playlist Geometry - PYTHAGOREAN THEOREM
Pappus' theorem and the cross ratio | Universal Hyperbolic Geometry 3 | NJ Wildberger
Pappus' theorem is the first and foremost result in projective geometry. Another of his significant contributions was the notion of cross ratio of four points on a line, or of four lines through a point. We discuss various important results: such as the Cross ratio theorem, asserting the
From playlist Universal Hyperbolic Geometry
Theorem of Pappus (KristaKingMath)
► My Applications of Integrals course: https://www.kristakingmath.com/applications-of-integrals-course Learn how to use the Theorem of Pappus to find the volume of a solid, in this particular case, a right circular cone. Theorem of Pappus tells us that volume is equal to area of the plane
From playlist Calculus II
Mechanical Engineering: Centroids & Center of Gravity (24 of 35) Pappus-Guldinus Theorem 1 Explained
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the first theorem of Pappus-Guldinius of finding the area of an object. Next video in this series can be seen at: https://youtu.be/ZQv-eF80FA0
From playlist MECHANICAL ENGINEERING 4 - CENTER OF GRAVITY
Pythagorean Theorem VIII (Bhāskara's visual proof)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) following essentially Bhāskara's proof (Behold!). This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. #math #manim #
From playlist Pythagorean Theorem
Pappus and Pascal | Elementary Mathematics (K-6) Explained 12 | NJ Wildberger
Continuing with our introduction to elementary projective geometry, meant for primary school students, we discuss two of the most famous theorems in mathematics: one due to Pappus of Alexandria around 300 A D and one due to Blaise Pascal in the 1600's. The first result only requires a piec
From playlist Elementary Mathematics (K-6) Explained