If I enter the expression
into my graphing calculator and then ask it for the fractional (rational) equivalent it cannot do so. Since the number is irrational it displays the first few decimal digits:
However, if I enter the expression
into the same graphing calculator and then ask it for the fractional equivalent it displays:
But this second number I entered is clearly not rational either.
What's going on?
The problem Isosceles Leg Length
uses the very similar number 85+42√2
which my calculator thinks is 47651/330
What is it about 42√2?
which implies the excellent approximation
√2 ≈ 19601/13860
1.414213562 ≈ 1.414213564
The fraction is actually one of the convergents to √2
Posted by Jer
on 2016-06-11 12:22:47