I. The Babylonian Mathematical Tablet known as Plimpton 322 written between 1900
ID: 3146045 • Letter: I
Question
I. The Babylonian Mathematical Tablet known as Plimpton 322 written between 1900 and 1600 B.C. provides sets of Pythagorean triples. One of the mathematical achievements over a millennium after e date of the Plimpton tablet was to show that for any integers u and v, a triple (a,b.c) defined by a-2uv, b-r-v2, c=u2+v2 is a Pythagorean triple. Prove it. 2. Describe the location (rivers) of and list some of inventions related to mathematics made by ancient . Babylonians, . Egyptians 3. Multiply 19 and 29 by two 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. 6. 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 where d is a diagonal of the rectangle xd = 65 Solve the problem.Explanation / Answer
'u' and 'v' are two integers.
We are given a= 2uv; b= u2 -v2 ; and c= u2 + v2 ;
We are to prove that (a,b,c) is a Pythagorean triplet.
If (a,b,c) is a pythagorean triplet then a2 + b2 = c2
Here
a2 + b2 = (2uv)2 + (u2 -v2)2
= 4 u2 v2 + u4 + v4 - 2u2v2
= u4 + v4 +2u2v2
= (u2)2 + (v2)2 + 2(u2)(v2)
This is of the form a2 + b2 + 2ab
Hence it can be written as :
(u2 +v2)2 = (c)2
Hence, we have proved that starting with a2 + b2 we arrived at c2 ;
Hence a2 + b2 = c2 ;
Thus, with this we can say that (a,b,c) are Pythagorean triplets;