Clear DefinitionsPythagorean Theorem
1 min read
Pronunciation
[pie-thag-uh-ree-uhn thee-uh-ree-uhm]
Analogy
Think of squares drawn on each side of a right triangle: the two smaller squares together have the same area as the largest square.
Definition
A fundamental principle in Euclidean geometry stating that in a right-angled triangle, the sum of the squares of the two legs equals the square of the hypotenuse.
Key Points Intro
The Pythagorean theorem relates the lengths of sides in right triangles.
Key Points
Formula: a² + b² = c² for a right triangle
Legs: the two shorter sides adjacent to the right angle
Hypotenuse: the side opposite the right angle
Applications: used for distance and coordinate calculations
Example
Calculating the straight-line distance between two blockchain nodes on a grid network using their x and y coordinates.
Technical Deep Dive
Proofs include algebraic methods, geometric rearrangements, and similarity of triangles. In coordinate geometry, the distance formula √((x₂−x₁)²+(y₂−y₁)²) directly derives from the theorem.
Caveat
Only applies in flat, Euclidean space—not on curved surfaces or non-Euclidean geometries.
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