Αποτελέσματα Αναζήτησης
Therefore, from didactic, historical, epistemological and foundational viewpoints, it is of significance to have a ‘visual’ and direct proof of Th ̄abit’s theorem in the same manner as the classics of Euclid and Pappus. In this article, we present such a proof. The paper is suitable for a wide variety of readers.
The proof of Thabit’s generalization is identical to one of the standard ways of proving the theorem of Pythagoras using similar triangles, and provides a very accessible generalisation with which to challenge learners.
the Pythagorean theorem is a special. case, one can write. 52 _|_ C2 = a2 _|_ 26c cos A. 2. Upon substituting for a, b, and c, respectively, in step 1, the result is: (AB)2 + (AC)2 = (BC)2 + 2(AB)(AC) cos A. 3. Since angle BAC = angle AC'B' = angle AB'C, then cos A = cos AB'C = cos AC'B'.
By the Pythagorean Theorem (applied twice), the expression |AB |2 + |AC |2 = b 2 + c 2 is equal to 2h 2 + (p + y)2 + (q + y)2. Since the Pythagorean Theorem also yields the equation y 2 + h 2 = r 2, it follows that b 2 + c 2 = 2r 2 – 2y 2 + (p + y) 2 + (q + y) 2 = p 2 + q 2 + 2 p y + 2q y + 2 r 2. Now consider the other side of the equation ...
His original contributions include proofs of the Pythagorean theorem, a proof of Menelaus's theorem, proofs of Euclid's fifth postulate, and work on composite ratios. Thābit's achievements in astronomy are closely linked to his work in mathematics.
Thabit ibn Qurra. Many people had commented on the Pythagorean Theorem, but Thabit ibn Qurra (b. 836 in Turkey, d. 02.18.901 in Iraq) was one of the first to offer commentary on it and create a new proof for it.
Thābit's work on amicable numbers and number theory helped him to invest more heavily into the Geometrical relations of numbers establishing his Transversal (geometry) theorem. [11] [16] Thābit described a generalized proof of the Pythagorean theorem. [17]
