Tuesday Puzzle

Re: Tuesday Puzzle

I believe I have solved it. I don't know that posting a numeric answer would spoil it for those still working on it, but just to hide it a little, I think the ratio Green:Orange:Yellow is 1:1.56:0.32

;-)

Re: Tuesday Puzzle

Been 45 years since I fooled with unit circles. Time enough to forget a lot.

Solution

Draw a line between the two points where all three colors meet. Then consider these three areas:

The circle: Area = pi

The small equilateral triangle: Height = 1.5, Area = 1.5^2 / sqrt(3)

The large equilateral triangle: Height = 2, Area = 2^2 /sqrt(3).

Then the areas in question are:

Green = 2/3 ( circle-small triangle) = 1.23

Orange = small triangle + Green /2 = 1.91

Yellow = large triangle - Orange = .40

Re: Solution

The area of the small triangle does not seem right.

I think it is 1.5*1.5/sqrt(3).

Re: Solution

Nikos, perhaps you are reading the ^ symbol as 'multiply'. I believe Alex is using it to mean 'exponent'. (It could be read either way in the next equation: 2^2). I believe you are using the * symbol as 'multiply'.

But using ^ as exponent, Alex's equation 1.5^2/sqrt(3) is the same as your equation 1.5*1.5/sqrt(3).

Correct

But if it shows up as clearly (not) on Niko's screen as on mine, the confusion could just be visual. I don't know another symbol as standard as "^" for "to the power". Maybe a double asterisk like I think some programming languages use?