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Anonymous1772099915
02-27 05:24
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Scholarly Encyclopedia (Detailed Definition) From the Encyclopædia Britannica: Pythagorean theorem states that in a right‑angled 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. In algebraic form: 𝑎 2 + 𝑏 2 = 𝑐 2 a 2 +b 2 =c 2 Here: 𝑎 a and 𝑏 b are the two sides that form the right angle 𝑐 c is the hypotenuse This theorem also has ancient historical references in Indian mathematics (Baudhayana Śulba‑sūtra) and early Babylonian tablets, even though it’s widely associated with Pythagoras. 📘 2. GeeksforGeeks (Practical Statement & Explanation) According to GeeksforGeeks: The theorem explains the relationship among the three sides of a right‑angled triangle. It says: In a right‑angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. This can be written as: hypotenuse 2 = base 2 + perpendicular 2 hypotenuse 2 =base 2 +perpendicular 2 So if you know any two sides of a right triangle, you can calculate the third. The article also includes a proof using similar triangles and the converse of the theorem (if the squares add up, the triangle is right‑angled). 📘 3. Historical and Cultural References The theorem we call Pythagoras’ was known in several ancient cultures before it was formally credited to Pythagoras: Ancient Chinese mathematical text Zhoubi Suanjing used a diagram (Xuan tu) to demonstrate the relationship between sides of a right triangle, especially the 3‑4‑5 case. This is an early geometric representation of the same principle — showing that the square on the hypotenuse equals the sum of the squares on the other two sides. Texts like The Nine Chapters on the Mathematical Art (China) and Baudhāyana Śulba‑sūtra (India) contain knowledge of these principles long before Greek documentation. Early mathematicians in multiple cultures explored right‑angled triangles and their relationships. 📘 4. Practical Example (Worked Solution) From typical academic explanations: If a right triangle has: base = 12 =12 perpendicular = 5 =5 Then according to the theorem: hypotenuse 2 = 12 2 + 5 2 = 144 + 25 = 169 hypotenuse 2 =12 2 +5 2 =144+25=169 So, hypotenuse = 169 = 13 hypotenuse= 169 =13 This shows how the theorem helps calculate an unknown side when the other two are known.
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Anonymous1772099915
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