35

Explanation: Bonus:


19

There are at least two possible ways to do this, depending on your definition of a polygon. 1: 2:


15

Lot of interesting answers here. My attempt was this: Admittedly, there are several pretty good definitions of corner which would not deem this as a solution.


11

First of all, note that So Here are two versions of this. First, But


10

I believe this is the highest score possible with 100 or fewer operations: 99 operations; Score > $10^{10^{10^{10^{10^{10^{10^{10^{10^{10^{10}}}}}}}}}}$ As the rather absurd score above suggests, arbitrarily large scores are possible. In particular, we can construct a sequence of approximations $A_k$ that converge extremely rapidly to $\pi$, giving scores ...


9

Following in the footsteps of @agnishom-chattopadhyay, here are a couple more ideas that rely on stretching the idea of what counts as a corner: The polygon on the left is so the midpoint counts as zero, one, two or four corners, entirely depending on your definition. (I don't think there's any reasonable way to count it as three, though.) The polygon on ...


7

I'd start by opening a private window in your browser. All major browsers offer this option nowadays. That might not be enough, since location can also have a great influence on your search (depending on context; the influence is greater when you search for 'restaurant' than for 'restaurant in Paris'). You might want to use a VPN to 'hide' your location from ...


7

Three fours, five operations, score 1.0413 $$ \sqrt[4!]{4!}+\sqrt{4} \approx 3.141586 $$ Also five operations but too cute not to include, score 0.7539: $$ \sqrt[4]{44\sqrt{\sqrt{4!}}} \approx 3.141423 $$ Four operations, score 0.7059: $$ \sqrt4^\sqrt{\log_4{44}} \approx 3.143093 $$ The best three-operation expression has already been posted in ...


6

Slightly simplifying Dark Malthorp's remarkable solution, we get: $$\pi \approx A_k = \left[1 - \left( 2 \cdot \log\lceil \sqrt{3!_k}\rceil + \sqrt{4}\right)\div(\lfloor\sqrt{\lceil\sqrt 5\rceil!_k}\rfloor!)\right]^{\lceil\sqrt{6!_{k-1}}\rceil!} \div \lfloor\sqrt 7\rfloor \cdot \lceil\sqrt{\lceil\sqrt 8\rceil!_k} \rceil!\cdot \lfloor\sqrt{\sqrt{9}!_k}\rfloor!...


5

Okay, I'll start us off with the obvious: Surely that can be improved on….


5

is equal to and scores which is $\approx0.4830$. Edit: Better yet is which scores , or $\approx0.5614$.


4

One possibility is to simply have a In the attached image one could argue that the building, if so designed, fits that criteria even though the outside of the building has only four corners. This is a technicality, only, but still..


3

Another solution is the answer to this age-old problem Where part of the the answer is This makes a For completeness, the other half of the answer to that riddle is A video explanation of both halves can be found here


3

Got it down to 3.14 but it uses sin again: Score: 1.38767676535 Ok this is extremely close with 2 ops. (3.18): Score: 0.71908465944 I'm not sure if this is legal cuz it uses sin: Score: 0.49654277813 Very close approximation (3.1): Score: 0.44995372319 Really simple one lol works surprisingly well: Score: 0.42447963952 Extremely close (3.16) but 4 ...


3

This isn't legal, but with a score of $+\infty$


3

3.160964... in 4 operations, score 0.42820978


3

If the trickery is in the word "polygon" one other option is to make it for example, a polygon but only have right angles


2

Now I've got it ! Just finished generating all possible solutions for a given number of operations. Had to discard some answers because of float overflow so I hope big numbers means lower score. Best scores up to 5 operations were found by Roman Odaisky and zixuan. Here's a solution for 6 operations : with a score of 0.86778360, but it's still less than ...


2

Only used $4-\frac{4}{4}$ operations and $4-\frac{4}{4}$ $4$s. Score: Please allow this answer. I took $4$ hours to find this answer (or a very long time).


1

Another alternative option is installing Google on a fresh device you have never used to search with and see the results this returns (e.g. installing the Google app on your phone without syncing your previous history).


1

Second answer, got it to 3.18 with 5 operations: Score = 0.276


1

If this is legal: Equals With 3 operations For a score of 0.187


1

The following query is worth 330 points:


1

Permutation puzzles are puzzles in which a random permutation needs to be restored to the identity permutation by using a limited (or 'clumsy') set of moves. For example, with the Rubik's cube, you would like to be able to swap two corners by themselves, but you can't do this directly - you can only rotate faces. A key feature is then to find - and ...


1

What about this? It only has 7 or 9 right angles so it should meet your requirements.


1

The Oxford English Dictionary gives, for 'polygon', the following definition: A plane figure with at least three straight sides and angles, and typically five or more. This is similar to the definition given by Cambridge University. These definitions allow for answers not obviously possible when using the stricter, more mathematical definition found in ...


1

I'm late to this party, and the OP seems to have left, but here's my 19-word solution! (Basically Lampost's accepted answer with some of the ending changed)


1

Do possessive nouns count? Also, is there a specific dictionary that the word has to be in? For S, the word "suss's" (4/5) would beat out "assess" and "sasses." If possessive nouns aren't allowed, then "susses" would tie for the record (4/6).


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