Date Grade Name I. The Babylonian Mathematical Tablet known as Plimpton 322 writ

Question

Date Grade Name I. The Babylonian Mathematical Tablet known as Plimpton 322 written between 1900 and 1600 B.C over a millennium after provides sets of Pythagorean triples. One of the the date of the Plimpton tablet ar-2in, b-u,-. c-ar2 is a Pythagorean triple. Prove it. was to show that for any integers u and v, a triple (a.be) defined by ancient 2. Describe the location (rivers) of and list some of inventions related to mathematics made by Babylonians, . Egyptians 3. Multiply 19 and 29 by twe methods employed by ancient Egyptians described in Rhind papyri. Check your answer using the modern way of multiplication 4. Divide 359 by 19 by the method employed by ancient Egyptians described in Rhind papyri. Check your answer using the modern way of division. 5. Present 2/5 in a way ancient Egyptians did. You can use modern notations. A group of Old Babylonian tablets was lifted at Susa. One of the problems of the Susa Tablets is similar to: Find the sides x and y of a rectangle, given Solve the problem. 6. xy 60 xd 65 e d is a diagonal of the rectan

Explanation / Answer

Pythagorean triples says that if three numbers a,b & c (such that c>a & c>b) comes under pythagorean triples then relation between the three numbers will be such that = a2+b2 = c2

now, for integers u & v, a,b & c are given below

a = 2uv

b = u2-v2

c = u2+v2

now using the pythagorean triple relationship

a2+b2=c2

(2uv)2+(u2-v2) = (u2+v2)2

now by solving left hand side equation the result will be as below

4u2v2 + u4+v4-2u2v2

= u4+v4 +2u2v2

now by solving right hand side equation the result will be as below

(u2+v2)2

= u4+v4+2u2v2

so, left hand side = right hand side

so, a,b & c are pythagorean triples

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