[Daily puzzle] Fun with geometry \ stacker news ~science

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[Daily puzzle] Fun with geometry

736 sats \ 4 comments \ @south_korea_ln 20 Oct 2024 science

Right angles are indicated with grey squares. The solution can be expressed as a fraction.

Good luck!

Previous iteration: #731084 (the solution was indeed Euler's constant $e$ , see #731144).

I will probably be slightly less regular this week in posting the puzzles, busy week ahead.

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300 sats \ 2 replies \ @Scroogey 20 Oct 2024

The small triangle at the bottom right must be right and isosceles, and the angle at the bottom right must be 45°, because the sum of angles is 180°.
This means the largest triangle is isosceles, and the bottom length is $4$ , i.e. the units are $\frac{1}{2}$ .

We begin with $z^{2} + z^{2} = 1$ giving $z^{2} = \frac{1}{2}$

The we continue to the left, looking at the small triangle with sides $y$ , $c$ , and $1$ :

y^{2} + c^{2} = 1

y^{2} + (5 - c)^{2} = 20

b = \frac{2}{20}

x^{2} + \frac{1}{5} = 1

x^{2} = \frac{4}{5}

Similarly we continue for $x$ and $w$ and get

\frac{17}{18} + \frac{5}{4} + \frac{100}{64} + \frac{2}{1} = \frac{47}{8}

0 sats \ 1 reply \ @Scroogey 20 Oct 2024

The last two $x^{2}$ should be $y^{2}$ . Is there a way to edit after 10 minutes?

1 sat \ 0 replies \ @south_korea_ln OP 20 Oct 2024

Can't edit after 10 minutes. Not sure the reason is technical or ideological.

0 sats \ 0 replies \ @nym 20 Oct 2024

1/( (4/5)^2 ) + 1/( (4/3)^2 ) + 1/( (4/2)^2 ) + 1/( (2√2)^2 ) = 5/2