1. G

    Archimedes’ Approximation to SQRT3

    Archimedes states that 1351/780 > SQRT3 > 265/153, but doesn’t say how he derived this. It struck me that Archimedes may have used geometry to get there, and I came up with a possible solution at Archimedes and the Square Root of Three, A Geometrical Approach. This suggests a general...
  2. A

    Find the modulus and argument of sqrt(3+i).

    I tried letting sqrt(3+i) = a+bi. With some calculations, I got 2a^2 = x + sqrt(x^2+y^2), 2b^2 = -x + sqrt(x^2+y^2), which means a = +- sqrt[(3+sqrt(10))/2] and b = +- sqrt[(-3+sqrt(10))/2]. Does this mean there are four possible answers? But then when I tried doing this by expressing the...
  3. shunya

    Prove 1+sqrt(3) is irrational

    Question) Prove that 1 + sqrt3 is an irrational number. Show similarly that m + n(sqrt3) is an irrational number for all rationals m and n (n not 0) In the question, sqrt3 means square root of 3. I will use the same notation everywhere in the question My attempt: We will assume (correctly)...