Opening questions…

The Baudhāyana-Pythagoras Theorem

Enable JavaScript to open the explanations.

Page 33: How can one construct a square having double the area of a given square? A first guess might be to simply double the…
Page 34: Why does the new dotted square have double the area of the original square? Can you draw some horizontal and…
Page 34: Why should the extension of the vertical and horizontal sides of the original square pass through the vertices of…
Page 35: Cut out two identical squares of paper. Draw, label, and cut Square 1 along both diagonals (making pieces 1, 2, 3,…
Page 36: Now suppose we are given a square, and we want to construct a square whose area is half that of the original square.…
Page 36: Cut out a square from a piece of paper. Now make a square whose area is half the area of the first square. Will the…
Page 37: Why is PQRS a square? Why is its area half that of the original paper?
Page 37: Find the hypotenuse of this isosceles right triangle.
Page 38: In the rest of this chapter, we will assume that all the lengths are of a fixed unit unless specified otherwise.…
Page 39: Will we ever get a number with a terminating decimal representation whose square is 2? Can √2 be expressed as a…
Page 39: Earlier, we saw a method to create a square with double the area of a given square paper. There is another method to…
Page 39: The length of the two equal sides of an isosceles right triangle is given. Find the length of the hypotenuse. Find…
Page 40: The hypotenuse of an isosceles right triangle is 10. What are its other two sidelengths?
Page 42: Why does Baudhāyana’s method work? Can you see why the method works in the case where the two squares are the same…
Page 44: The 4-sided figure obtained (T + U + V) is in fact a square with an area equal to the sum of the areas of the two…
Page 45: Cut out and join two different sized squares (sides a and b). Make two cuts to make three pieces. Rearrange the…
Page 47: Make a right-angled triangle in your notebook whose shorter sidelengths are 3 cm and 4 cm. Now, measure the length…
Page 47: If a right-angled triangle has shorter sides of lengths 5 cm and 12 cm, then what is the length of its hypotenuse?…
Page 47: If a right-angled triangle has a short side of length 8 cm and hypotenuse of length 17 cm, what is the length of the…
Page 47: Using the constructions you have now seen, how would you construct a square whose area is triple the area of a given…
Page 47: Let a, b and c denote the length of the sides of a right triangle, with c being the length of the hypotenuse. Find…
Page 48: List down all the Baudhāyana triples with numbers less than or equal to 20.
Page 48: Is there an unending sequence of Baudhāyana triples? We have seen that (3, 4, 5) is a Baudhāyana triple. Is (30, 40,…
Page 48: Do you see any pattern among them? Can we form a conjecture on Baudhāyana triples based on this observation? Is this…
Page 49: If (a, b, c) is a Baudhāyana triple, then (ka, kb, kc) is also a Baudhāyana triple where k is any positive integer.…
Page 49: Is (5, 12, 13) a primitive Baudhāyana triple? What are the other primitive Baudhāyana triples with numbers less than…
Page 49: Generate 5 scaled versions of each of these primitive triples. Are these scaled versions primitive?
Page 49: If (a, b, c) is non-primitive, and the integers have f — greater than 1 — as a common factor, then is (a/f, b/f,…
Page 50: For this, we need to know the nth odd number. What is it? What is the sum of the first (n − 1) odd numbers? If the…
Page 50: Find 5 more Baudhāyana triples using this idea.
Page 50: Does this method yield non-primitive Baudhāyana triples?
Page 50: Are there primitive triples that cannot be obtained through this method? If yes, give examples.
Page 51: Given everything you’ve just learned in this chapter about Baudhāyana triples, why is n = 2 so special that this…
Page 52: The lotus-flower problem from Bhāskarāchārya’s Līlāvatī — find the depth of the lake.
Page 52: Find the diagonal of a square with sidelength 5 cm.
Page 52: Find the missing sidelengths in the following right triangles: (a) legs 7 and 9 (b) leg 4, hypotenuse 10 (c) leg 40,…
Page 53: Find the sidelength of a rhombus whose diagonals are of length 24 units and 70 units.
Page 53: Is the hypotenuse the longest side of a right triangle? Justify your answer.
Page 53: True or False — Every Baudhāyana triple is either a primitive triple or a scaled version of a primitive triple.
Page 53: Give 5 examples of rectangles whose sidelengths and diagonals are all integers.
Page 53: Construct a square whose area is equal to the difference of the areas of squares of sidelengths 5 units and 7 units.
Page 53: (i) Using the dots of a grid as the vertices, can you create a square that has an area of (a) 2 sq. units, (b) 3 sq.…
Page 54: Find the area of an equilateral triangle with sidelength 6 units.
Page 54: There are 3 closed boxes — one containing only red balls, the second containing only blue balls and the third…

Back to Mathematics