Articles containing proofs | Area | Theorems in plane geometry | Pythagorean theorem | Angle | History of geometry | Proof without words | Euclidean plane geometry
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation: The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared distance between two points equals the sum of squares of the difference in each coordinate between the points. The theorem can be generalized in various ways: to higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and to objects that are not triangles at all but n-dimensional solids. The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power; popular references in literature, plays, musicals, songs, stamps, and cartoons abound. (Wikipedia).
Converse Pythagorean Theorem & Pythagorean Triples
I explain the Converse Pythagorean Theorem and what Pythagorean Triples are. Find free review test, useful notes and more at http://www.mathplane.com 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/Profro
From playlist Geometry
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
Proofs of the Pythagorean Theorem
The Pythagorean Theorem appears in nearly every branch of mathematics. Here are several proofs drawing from algebra, geometry, and trigonometry.
From playlist Lessons of Interest on Assorted Topics
This geometry video tutorial provides a basic introduction into the pythagorean theorem. It explains how to use it to find missing sides and solve for x. In addition, it provides examples of solving word problems using pythagorean theorem for shapes such as right triangles, squares, rhom
From playlist Geometry Video Playlist
Pythagorean theorem - What is it?
► My Geometry course: https://www.kristakingmath.com/geometry-course Pythagorean theorem is super important in math. You will probably learn about it for the first time in Algebra, but you will literally use it in Algebra, Geometry, Trigonometry, Precalculus, Calculus, and beyond! That’s
From playlist Geometry
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
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
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
Episode 3: The Theorem Of Pythagoras - Project MATHEMATICS!
Episode 3. The Theorem of Pythagoras: Several engaging animated proofs of the Pythagorean theorem are presented, with applications to real-life problems and to Pythagorean triples. The theorem is extended to 3-space, but does not hold for spherical triangles. A Program Guide and Workbook
From playlist Courses and Series
Pythagorean Theorem - Understand In 10 Minutes
The Pythagorean Theorem is a very important law in geometry that allows us to find the sides of right triangles. In this video I will go the Pythagorean Theorem formula and will solve various Pythagorean Theorem problems. If you need extra help with math check out my math learning program
From playlist Pre-Algebra
Let’s Get To Know The Pythagorean Theorem….Step-by-Step….
TabletClass Math: https://tcmathacademy.com/ Math help with the Pythagorean Theorem. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes: https://tabletclass
From playlist GED Prep Videos
Pythagorean Party by Karen Campe
Karen Campe will guide you through a series of interactive activities in GeoGebra that will help you understand the Pythagorean Theorem and its applications. You'll also explore Pythagorean Triples and dive into the Converse Pythagorean Theorem by using GeoGebra to explore this theorem and
From playlist FLGGB 2023
Is a triangle with sides 3, 4, 5 a right triangle? Let’s find out…
How to determine if a triangle is a right triangle by using the Pythagorean Theorem. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable
From playlist GED Prep Videos
Physical Science 2.4b - The Pythagorean Theorem
A simple introduction to the Pythagorean Theorem, along with an example, and some comments on the Pythagoreans.
From playlist Physical Science Chapter 2 (Complete chapter)
Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]
Calcea Johnson and Ne’Kiya Jackson are two high school students at St. Mary's Academy in New Orleans who recently presented a new proof of the Pythagorean theorem at the Spring Southeastern Sectional Meeting of the American Mathematical Society. There are, of course, many proofs of the Pyt
From playlist Math Minutes
Why does the Pythagorean Theorem Work? #SoME1
Some exploration of the Pythagorean Theorem and why it works.
From playlist Summer of Math Exposition Youtube Videos
In this video, we present a geometric proof of the Pythagorean theorem. This famous theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Our proof utilizes the prin
From playlist Shorts
The Pythagorean Theorem I: Two Proofs and a Corollary
Are you interested in math or physics tutoring for you or someone you know? Please check out my website for more details of my registered business, or give me a call or email anytime! https://www.whatthehectogon.com/ +1 (973) 597-8775 sam@whatthehectogon.com In this video lesson, I intr
From playlist Geometry