For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
11/12/2008

FOR STUDENTS

PROBLEM # 1
A circle passes through the three vertices of an isoceles triangle that has two sides of length 3 and abase of length 2. Find the area of this circle?

FOR GROWNUPS

PROBLEM #2
Note that (2^0.5-1)¹ = 2^0.5 - 1^0.5 and that (2^0.5-1)² = 2 - 2 x 2^0.5 + 1

= 9^0.5 - 8^0.5.

Prove that for all positive integral values of n there exists an integral value of m such that

(2^0.5-1)ⁿ = m^0.5 - (m-1)^0.5.

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Problem Solutions 10/30/08

PROBLEM # 1
The sum of Ramu and Shyamu's age is 40. The sum of Shamu's age and Chotu's age is 34. The sum of Ramu's age and Chotu's age is 42. How old is Ramu?

Solution:

24.

FOR GROWNUPS
If R(t) = integral of sec²(x) + sec(x).tan(x) from 0 to t, then determine
R" (pi/4).

Solution:
3 sqrt(2) + 4.

Congratulations to Aseem Chandawarkar, Shailesh Goregoankar, Prabhakar Nadkarni, Dhruv Ramanujan and Vinod Samala, who were winners of the last set of puzzles.

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