Taat
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Last Posted July 17, 2025 at 3:38 PM
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#25 Math problem IQ test in Off Topic
toads_tfnegative area square?

negative area makes sense if you consider it as the "area under a function" (so a defined integral of a function)
and you could just handwave it anyways.

This looks like a "find the overlapping area of three circles" question. It's extremely tedious, but pretty braindead with a symbolic calculator

Here's a very rough outline of how to find A3 (not wasting any more time on this):

Show Content
let's start with an A_s (assuming it's the outer square) of 1 and multiply by the actual A_s at the very end
https://i.imgur.com/2GSGwQ1.png
I guessed that the vague curves are sections of circle with center at a corner of the large square and radius the same as the square's side length
https://i.imgur.com/qny2VWS.png
the program gives the equations for the circles easily
https://i.imgur.com/mzP36RE.png
change the relevant half of the circle into a y=f(x) format
https://i.imgur.com/y15qo1k.png
https://i.imgur.com/53bLMWX.png
find the intersections of the relevant curves, and use them as the bounds of the defined integrals..
https://i.imgur.com/VqDoIGT.png
and just smack the integrals into a calculator, and you add them all together:

+ integral_(3/8 - sqrt(7)/8)^(1 - sqrt(3)/2) (sqrt(2 x - x^2) dx

- integral_(3/8 - sqrt(7)/8)^(1 - sqrt(3)/2) (sqrt(2 x - x^2) + 1/2 (-1 + 2 sqrt(x - x^2))) dx

+ integral_(1 - sqrt(3)/2)^(5/8 - sqrt(7)/8) 1/2 (1 - 2 sqrt(x - x^2)) dx

- integral_(1 - sqrt(3)/2)^(5/8 - sqrt(7)/8) 1/2 (1 - 2 sqrt(x - x^2)) dx

+ integral_(5/8 - sqrt(7)/8)^(1/2) (1 - sqrt(2 x - x^2)) dx

- integral_(5/8 - sqrt(7)/8)^(1/2) (1 - sqrt(1 - x^2)) dx
and multiply the result by the side length
and the final answer for A3 (unless I made mistakes....)

surprise, it's a massive clusterfuck:
(-47)*(9/64 - sqrt(3)/8 - (5 π)/12 + tan^(-1)(4 + sqrt(7)) + 1/64 (-17 + 16 sqrt(3) - 4 sqrt(7) - 8 sqrt(14 sqrt(3) - 24) - 16 sin^(-1)(3^(1/4)/sqrt(2)) + 16 csc^(-1)((2 sqrt(5 - sqrt(7)))/3)) + (1/64 (sqrt(321 + 48 sqrt(7) - 48 sqrt(43 + 16 sqrt(7))) + 8 (-3 + 4 sqrt(3) - sqrt(7) + 8 cot^(-1)(3/sqrt(31 + 8 sqrt(7))))) - (5 π)/12) - (1/64 (-9 + 16 sqrt(3) - 4 sqrt(7) - 8 sqrt(14 sqrt(3) - 24) - 16 sin^(-1)(3^(1/4)/sqrt(2)) + 16 csc^(-1)(2 sqrt(3 - sqrt(7))))) + (-1/64 sqrt(321 + 48 sqrt(7) - 48 sqrt(43 + 16 sqrt(7))) + π/3 + 1/8 (-1 + sqrt(7) - 8 cot^(-1)(3/sqrt(31 + 8 sqrt(7))))) - (1/192 (3 - 24 sqrt(3) + 24 sqrt(7) + 32 π - 96 cos^(-1)(1/8 (5 - sqrt(7))))))

= ~0.036566432691702221271670 - 0.019630731925696712432468 + 0.061918112844524846486709 - 0.0150274870976263361702352 + 0.04230790314076436373846 - 0.0173897792991522791591702

= 0.0887444503545161037349656 * (-47)
= ~-4.1709891666622568755433832..

and then just do that two more times for the final answer. It's not going to get much shorter.
Of course the question is pretty vague so this could be the solution to the wrong problem.
posted about 5 years ago
#8 delet this in TF2 General Discussion

https://i.imgur.com/TIPGxIP.png

Ftfy

posted about 5 years ago
#39 "who are you?" in TF2 General Discussion
Matthesits me!! im telling you to shut the fuck up!!!

11 hours ago
2 hours ago
36 minutes ago
30 minutes ago
1 minute ago

posted about 5 years ago
#24 MGE gods in TF2 General Discussion

https://www.youtube.com/watch?v=61naK3MVpCQ

posted about 5 years ago
#2 CSGO Key Change in CS2 General Discussion

There just won't be a central currency.. they keys that already exist will prob increase in value so it won't make traders quit

posted about 5 years ago
#5 Find your preferred damage-batching interval in TF2 General Discussion

Wait winger fires slower than pistol? What??

posted about 5 years ago
#3 issue with your computer is blocking the vac syste in TF2 General Discussion

Maybe it's the same thing as this?

https://www.reddit.com/r/GlobalOffensive/comments/d4isl1/psa_valve_messed_up_the_latest_steam_update_heres/

posted about 6 years ago
#8 new thrasher merch in Music, Movies, TV

Apparently it's bad enough that my browser thinks it's better that I just see a black screen

posted about 6 years ago
#13 what's a worse addiction to have? in Off Topic
jimmijwhat about smokking dick

As long as it's not your own dick it's fine

posted about 6 years ago
#3 code please in TF2 General Discussion

YSBjb2Rl

posted about 6 years ago
#85 Leagues meet to discuss future of North American TF2 in News
YeeHawwhere did rgl even get that much money? if it's from sponsors that's impressive but how is that much money possibly sustainable every season regardless of where it's from

The same way as esea.. pay to play

posted about 6 years ago
#23 why is /teleport a common bind in Off Topic

why do people sometimes call medic even when their med is dead? Is it supposed to be funny?

posted about 6 years ago
#20 School Project in Off Topic

It's a spambot necro

posted about 6 years ago
#11 circle in Off Topic

That's not a circle.

posted about 6 years ago
#3 17.9 lerp mastercomfig? in TF2 General Discussion

with 15.2 the client has zero time to do some part of interpolation, it's forced to push it within 1 tick perfectly. the 2.5 extra ms you get with 18 ms is usually enough time to make it as smooth as 30.3 ms (if you have a good connection and the server isn't struggling to run the game) without having much of an effect on the latency.

posted about 6 years ago
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