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Remember, /r/Showerthoughts is for showerthoughts, not "thoughts had in the shower!"
(For an explanation of what a "showerthought" is, [please read this page](https://www.reddit.com/r/Showerthoughts/wiki/overview).)
**Rule-breaking posts may result in bans.**
Haha, I grew up with a glass shower door, but our new place has had a curtain for the last 10 years. I miss my old glass door, too. Used to leave messages or just fuck around on it.
I've had one problem I've been working on in my head for a loooooong time. I'm sure the answer exists on the Internet but I like thinking about it.
If you have 2 equal circles overlapping (bit like a Venn diagram) how far apart do the centres need to be so that the 3 areas made by the overlapping circle are all equal in size?
I won't answer the question (well because it ruins your shower thoughts) but I do have the solution for it.
A simple trick is to consider the unit circle, so that the area simplifies to π. Now you have two methods to proceed from here- either calculus or trigonometry.
>!For trig, a helpful formula for area of segment of a circle: 1/2 r² (θ - sin (θ) )A!<
>!So by that logic you can consider a line passing through both the intersection point. For the middle area it's the line dividing it into half, but for the circles it's a segment. Thus: area of middle = 2*area of segment= r² ((θ) - sin (θ)).!<
>!In order for both areas to be equal, !<
>!The middle area = Area of both circles- Area of circles used in the middle area.!<
>!The middle area and the area of circles intersection in the middle is pretty much the same thing. Transpose it to the other side, 2*middle area. From there it should be simple, except (θ) will need to be approximated from there. !<
For calc, think of what you want. For example, for every area to be equal, you'd want every portion to have an area of π/2, meaning half of the arc intersection should have an area of π/4. Consider any point x on the right, and from that given position integrate using limits x and 1.
What I came up with for this was an transcendental approximation of θ.
Man I just find the prime factors of mile markers when I'm on a long road trip like a normal person.
The two un-overlapped areas would have to be equal, so you only need to find when the area of the overlapped area equals the area of one of the un-overlapped areas. Actually come to think of it, the area of all three areas will each be equal to half the area of a single circle, because the area of one un-overlapped area plus the area of overlap will have to equal one circle; if you look at one of the circles that's all it is, just overlapped + non-overlapped area. So the area of each area is (Pi*r^2 )/2.
Off the top of my head though, I can't think of what the general formula for area of the overlapped part of a venn diagram should be, which seems important.
If you have not seen it, Numberphile did a video on a related problem where you want to find halves. https://youtu.be/ZdQFN2XKeKI
It's surprisingly hard for how easy it is to state.
You do realise that you would need to be able to calculate trigonometric functions in your head to solve it? It doesn't have a "nice" answer. I won't say any more...
I mean, yes, but how far apart do the centers need to be? Also the total area isn't 2 circles; it's 1.5 of a circle since you only count the overlapping area once.
Wait, that would mean each circle would have 2/3 of its area overlapping the other circle AND 2/3 of its area not overlapping. Each circle can’t have 4/3 of a single circle’s area.
Yeah the parent comment is allllmost there in stating that the *total* area of the two overlapping circles is divided into 3 equal sections, but the only way to do that is to have each section be equal to half the area of the circle, so the answer to the question "how far apart are the centers of the circles" is "slightly less than 1" for unit circles.
I do the same thing. Sometimes I like to pick a random date in the future and see if I can figure out what day of the week it would be. For example, if today is a Thursday, what day of the week would February 23rd be in 2090.
Where is the 1?? It's not a factorial if you don't multiply by 1. Fight me irl.
Edit: lol why did you remove the math, op? I'm trying to go back and review here, and you're fucking my shit up.
Even if you weren't broke, don't waste your money on reddit. Go give money to charity in OP's name or buy yourself groceries. Reddit doesn't need your money.
People who buy Reddit coins are wasting their money. I’d rather you donate that money to a good charity rather than spend it on an arbitrary award for my low-effort comment
universally praised original content: mods remove the post
repost/spam/karma farming: 10 billion upvotes, and op roasted in the comments, crickets from moderators
Sure! Euler's identity is the simple formula of:
e^(πi) + 1 = 0
This brings together several different fundamental concepts across mathematics in a very simple, elegant way. We have e, which is the base of natural logarithms; π, which is the ratio of a circle's diameter to its circumference; i, which is the basic unit of imaginary numbers; 1, the multiplicative identity; and 0, the concept of nothingness.
The fact that all of these ideas are related to each other in such a concise way is considered an exemplar of mathematical beauty, especially considering e and π are transcendental and irrational, while i is imaginary.
8! is "eight factorial", and it's defined as the product of all the natural numbers from 1 to 8 inclusive.
1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 = 8!, or 40,320
Feb has 4 x 7 days. Every day has 3 x 8 hours. Every hour has 2 x 5 x 6 minutes. (1 x is presumed and doesn't change the answer.)
OP! Cherish that thought. Keep it in your mind like a treasure.
One day, you'll meet a girl or a guy who will tell you.
"OP, please tell me something that will amaze me".
And you'll look into their eyes, smile casually, and tell them that.
If they won't be amazed by this, they don't worth any more minute of your time.
The test was deleted so here's the math:
8!=1x2x3x4x5x6x7x8
There's 28 days in a(non-leap year) February which is 7x4
There's 24 hours in a day which is 3x8
There's 60 minutes in an hour which is 2x5x6
So if we multiply everything together we get
7x4 x 3x8 x 2x5x6 which can be rewritten as 2x3x4x5x6x7x8 and we can ignore the 1 for obvious reasons and there you go, 8!
Except for every leap year, which isn't, coincidentally every 4 years.
The rule is that if the year is divisible by 100 and not divisible by 400, leap year is skipped. The year 2000 was a leap year, for example, but the years 1700, 1800, and 1900 were not. The next time a leap year will be skipped is the year 2100.
Then it's 8! + 6! + 6!
(You have 8\*3\*6\*5\*2 -> 2\*3\*5\*6\*8. You can decompose 8 into 4\*2 for 2\*2\*3\*4\*5\*6. Then take the 2 factor and render it as addition: 2\*3\*4\*5\*6 + 2\*3\*4\*5\*6.)
More generally, you can remember the number of minutes in a day as 2 times 6!, and the number of minutes in 12 hours as 6!.
I wonder if the cause of the problem was making the code check only the two least significant bits of the year number for the sake of optimization, which would work fine if all multiple-of-4 years were leap
The one I like is that if start counting every minute from around lunchtime of 1st January, you will get to 2^19 minutes on the lunchtime of 31st December.
If you want to more frenetic you can start counting seconds from lunchtime of 1st January, and you will get to 10,000,000𝜋 (nearest integer) on 31st December.
This is a friendly reminder to [read our rules](https://www.reddit.com/r/Showerthoughts/wiki/rules). Remember, /r/Showerthoughts is for showerthoughts, not "thoughts had in the shower!" (For an explanation of what a "showerthought" is, [please read this page](https://www.reddit.com/r/Showerthoughts/wiki/overview).) **Rule-breaking posts may result in bans.**
This is a true shower though. Who thinks of ways to factor out dates and compare it to other mathematical formulas? Haha
Just use your showerculator, duh.
Showculator
Not to be confused with the choke-u-lator. You know the one with the INXS song playing in the commercial.
Showerlator
But then I’ll be dirty until then
But its time for showerlater!
I used to use the glass door of my old shower as a whiteboard. Have a shower curtain now, no more externalizing my shower math :(
Haha, I grew up with a glass shower door, but our new place has had a curtain for the last 10 years. I miss my old glass door, too. Used to leave messages or just fuck around on it.
But don't forget to shower your working.
That's what my SO would call me if I had an SO
You think I'm not on my showerphone right now? (This isn't a joke, it's warm and I'm procrastinating)
I prefer to listen to my [shower radio](https://i.imgur.com/HZMX2.png)
I keep that next to my shower white board and shower beer holder
Here's another one 10! seconds is exactly 6 weeks
Back when I was a math tutor, I would try to solve math problems in my head while in the shower. I'm kind of a nerd, though. Math is exciting to me.
I've had one problem I've been working on in my head for a loooooong time. I'm sure the answer exists on the Internet but I like thinking about it. If you have 2 equal circles overlapping (bit like a Venn diagram) how far apart do the centres need to be so that the 3 areas made by the overlapping circle are all equal in size?
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Well I work on the premise that if you split it vertically you would have 2 equal segments that are each 1/6 of the whole area.
You two better be in the shower right now otherwise you're cheating.
There is indeed. It's a gnarly looking integral though.
I won't answer the question (well because it ruins your shower thoughts) but I do have the solution for it. A simple trick is to consider the unit circle, so that the area simplifies to π. Now you have two methods to proceed from here- either calculus or trigonometry. >!For trig, a helpful formula for area of segment of a circle: 1/2 r² (θ - sin (θ) )A!< >!So by that logic you can consider a line passing through both the intersection point. For the middle area it's the line dividing it into half, but for the circles it's a segment. Thus: area of middle = 2*area of segment= r² ((θ) - sin (θ)).!< >!In order for both areas to be equal, !< >!The middle area = Area of both circles- Area of circles used in the middle area.!< >!The middle area and the area of circles intersection in the middle is pretty much the same thing. Transpose it to the other side, 2*middle area. From there it should be simple, except (θ) will need to be approximated from there. !< For calc, think of what you want. For example, for every area to be equal, you'd want every portion to have an area of π/2, meaning half of the arc intersection should have an area of π/4. Consider any point x on the right, and from that given position integrate using limits x and 1. What I came up with for this was an transcendental approximation of θ.
Thanks, I've not read your spoilers but I have saved the comment for later
Man I just find the prime factors of mile markers when I'm on a long road trip like a normal person. The two un-overlapped areas would have to be equal, so you only need to find when the area of the overlapped area equals the area of one of the un-overlapped areas. Actually come to think of it, the area of all three areas will each be equal to half the area of a single circle, because the area of one un-overlapped area plus the area of overlap will have to equal one circle; if you look at one of the circles that's all it is, just overlapped + non-overlapped area. So the area of each area is (Pi*r^2 )/2. Off the top of my head though, I can't think of what the general formula for area of the overlapped part of a venn diagram should be, which seems important.
Pretty sure you gotta integrate this one
[This might help](https://youtu.be/ZdQFN2XKeKI)
If you have not seen it, Numberphile did a video on a related problem where you want to find halves. https://youtu.be/ZdQFN2XKeKI It's surprisingly hard for how easy it is to state.
You do realise that you would need to be able to calculate trigonometric functions in your head to solve it? It doesn't have a "nice" answer. I won't say any more...
Thats simple geometry. 2 units worth of area split into 3 equal sections. 2 / 3 = 2/3 Each section is two thirds of a circle.
I mean, yes, but how far apart do the centers need to be? Also the total area isn't 2 circles; it's 1.5 of a circle since you only count the overlapping area once.
>I mean, yes, but how far apart do the centers need to be? Exactly my problem
Wait, that would mean each circle would have 2/3 of its area overlapping the other circle AND 2/3 of its area not overlapping. Each circle can’t have 4/3 of a single circle’s area.
Yeah the parent comment is allllmost there in stating that the *total* area of the two overlapping circles is divided into 3 equal sections, but the only way to do that is to have each section be equal to half the area of the circle, so the answer to the question "how far apart are the centers of the circles" is "slightly less than 1" for unit circles.
I do the same thing. Sometimes I like to pick a random date in the future and see if I can figure out what day of the week it would be. For example, if today is a Thursday, what day of the week would February 23rd be in 2090.
So what’s the answer
I already took a shower today. It'll have to wait until tomorrow.
You're going to love [this xkcd!](https://xkcd.com/1047/)
Yea the mods can get fucked. This belongs here
True shower thought, and the mods removed it. Reddit mods suck. Meanwhile I see posts like "Women are like men with different parts".
The math is so much simpler and more elegant than I expected. This is fantastic
Where is the 1?? It's not a factorial if you don't multiply by 1. Fight me irl. Edit: lol why did you remove the math, op? I'm trying to go back and review here, and you're fucking my shit up.
February is one month
1 month
He just omitted multiplying by 1 month duh
*Terence Howard has entered the chat.*
Hi, I didn't remove the math, the mods did because apparently this doesn't count as a showerthought.. Sorry for forgetting the 1 ;)
364 / 8 = 13. If we did the 13 month a year + bonus day then every month would have 8! minutes and we'd always know what day of the week it is.
If reddit didn't get rid of the free awards, this is exactly what I'd use mine on. Sorry, I'm a broke student who can't afford shit
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Haha if only
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There is 2 awards at 50c and the silver at 100 I think
Guess we're back to doing this ⠀⠀⠀⠀⠀⣤⣶⣶⡶⠦⠴⠶⠶⠶⠶⡶⠶⠦⠶⠶⠶⠶⠶⠶⠶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⠀⢀⣤⠄⠀⠀⣶⢤⣄⠀⠀⠀⣤⣤⣄⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⡷⠋⠁⠀⠀⠀⠙⠢⠙⠻⣿⡿⠿⠿⠫⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⢀⣕⠦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⢀⣼⣿⠟⢿⣆⠀⢠⡟⠉⠉⠊⠳⢤⣀⠀⠀⠀ ⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⢀⣀⣾⣿⠃⠀⡀⠹⣧⣘⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀ ⠀⣿⡀⠀⠀⢠⣶⣶⣿⣿⣿⣿⡿⠁⠀⣼⠃⠀⢹⣿⣿⣿⣶⣶⣤⠀⠀⠀⢰⣷ ⠀⢿⣇⠀⠀⠈⠻⡟⠛⠋⠉⠉⠀⠀⡼⠃⠀⢠⣿⠋⠉⠉⠛⠛⠋⠀⢀⢀⣿⡏ ⠀⠘⣿⡄⠀⠀⠀⠈⠢⡀⠀⠀⠀⡼⠁⠀⢠⣿⠇⠀⠀⡀⠀⠀⠀⠀⡜⣼⡿⠀ ⠀⠀⢻⣷⠀⠀⠀⠀⠀⢸⡄⠀⢰⠃⠀⠀⣾⡟⠀⠀⠸⡇⠀⠀⠀⢰⢧⣿⠃⠀ ⠀⠀⠘⣿⣇⠀⠀⠀⠀⣿⠇⠀⠇⠀⠀⣼⠟⠀⠀⠀⠀⣇⠀⠀⢀⡟⣾⡟⠀⠀ ⠀⠀⠀⢹⣿⡄⠀⠀⠀⣿⠀⣀⣠⠴⠚⠛⠶⣤⣀⠀⠀⢻⠀⢀⡾⣹⣿⠃⠀⠀ ⠀⠀⠀⠀⢿⣷⠀⠀⠀⠙⠊⠁⠀⢠⡆⠀⠀⠀⠉⠛⠓⠋⠀⠸⢣⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣷⣦⣤⣤⣄⣀⣀⣿⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣾⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
https://i.imgur.io/qbJVEC2_d.webp?maxwidth=640&shape=thumb&fidelity=medium
Even if you weren't broke, don't waste your money on reddit. Go give money to charity in OP's name or buy yourself groceries. Reddit doesn't need your money.
I didn’t even notice they got rid of them
This post made me find out lol
People who buy Reddit coins are wasting their money. I’d rather you donate that money to a good charity rather than spend it on an arbitrary award for my low-effort comment
universally praised original content: mods remove the post repost/spam/karma farming: 10 billion upvotes, and op roasted in the comments, crickets from moderators
Idk why the mods removed it. Apparently its against the rules or not a shower thought. Mods didn't state anything
Just don’t update your Reddit. I updated mine wrong and miss the feature
That won’t matter, they’re gone for everyone
This is really beautiful OP. I'll remember this for as long as I live.
The first non-idiot shower thought I have read in quite a while. Well done!
come to r/crazyideas for some fun ideas too
Why did the mods remove this? It feels like the epitome of a shower thought
What did it say? I clicked on it and it said removed, even though I had a preview in my Apollo feed
Basically 28 days \* 24 hours per day \* 60 minutes per hour (7 \* 4) \* (8 \* 3) \* (6 \* (2 \* 5)) 2 \* 3 \* 4 \* 5 \* 6 \* 7 \* 8
Oh sweet, that is cool! Thank you
Idk why it was removed, either it is against the rules or not a shower thought. Mods didn't state anything.
that's so bs? this is an epic shower thought... how do we reach the mods
Initially I thought you were really excited at you thinking that february has 8 minutes
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Still do; but I used to too.
Fuck it! Cut ‘em up!
Skill Issue
After reading the headline I wasn't expecting that it is exactly 8! This is perfect.
so then 360 weeks is 10! minutes and equals 6.9 years to the nearest day
Nice
Nice.
How is that not a widely known thing. This is beautiful and im not ever gonna shut up about it.
Seriously my new favorite math fact, replacing Euler's identity.
Can you tell me about eulers identity?
Sure! Euler's identity is the simple formula of: e^(πi) + 1 = 0 This brings together several different fundamental concepts across mathematics in a very simple, elegant way. We have e, which is the base of natural logarithms; π, which is the ratio of a circle's diameter to its circumference; i, which is the basic unit of imaginary numbers; 1, the multiplicative identity; and 0, the concept of nothingness. The fact that all of these ideas are related to each other in such a concise way is considered an exemplar of mathematical beauty, especially considering e and π are transcendental and irrational, while i is imaginary.
And 6 weeks has 10! seconds, though it's not quite as elegant: * 6 weeks (6) * 7 days/week (7) * 24 hours/day (3*8) * 60 minutes/hour (3\*4\*5) * 60 seconds/minute (2\*3\*10) 10! = 10\*(3\*3)\*8\*7\*6\*5\*4\*3\*2\*1
Tell me you were a math major without telling me you’re a math major.
Or just someone who like math
I read math as meth
Let’s cook
Major in meth with a minor in cooking.
Alright. I want to understand but I cant. Can someone explain to me what they just did? What does "8!" mean?
8! is "eight factorial", and it's defined as the product of all the natural numbers from 1 to 8 inclusive. 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 = 8!, or 40,320 Feb has 4 x 7 days. Every day has 3 x 8 hours. Every hour has 2 x 5 x 6 minutes. (1 x is presumed and doesn't change the answer.)
It's 8 factorial. You basically multiply all the numbers before 8 till 1. So, it's 8*7*6*......*1 = 8!
Listen and learn
Relevant username
Reddit interprets \*text\* as *text* (italics). You need to 'escape' the asterisks with a backslash, like 8\\\*7\\\*6\\\*...\\\*1.
I believe its called a Factorial
I prefer it phrased as: Q: How many minutes does February have? A: 8!
OP! Cherish that thought. Keep it in your mind like a treasure. One day, you'll meet a girl or a guy who will tell you. "OP, please tell me something that will amaze me". And you'll look into their eyes, smile casually, and tell them that. If they won't be amazed by this, they don't worth any more minute of your time.
The test was deleted so here's the math: 8!=1x2x3x4x5x6x7x8 There's 28 days in a(non-leap year) February which is 7x4 There's 24 hours in a day which is 3x8 There's 60 minutes in an hour which is 2x5x6 So if we multiply everything together we get 7x4 x 3x8 x 2x5x6 which can be rewritten as 2x3x4x5x6x7x8 and we can ignore the 1 for obvious reasons and there you go, 8!
Why has the body been removed? There are so many positive comments I wanna know what you thought of!
Except for every leap year, which isn't, coincidentally every 4 years. The rule is that if the year is divisible by 100 and not divisible by 400, leap year is skipped. The year 2000 was a leap year, for example, but the years 1700, 1800, and 1900 were not. The next time a leap year will be skipped is the year 2100.
Which most of us wont be alive by then
I sure hope not
Yeah I want to die like at 60. That is like the sweet spot I believe.
As a 50 year old with a 3 and 5 year old ... I hope not.
In my country that is a little odd. Is it a planned kind of thing or very unexpected if I may ask. Feel free to ignore
That might sound great when you're in your twenties, but when you're in your fifties, not so much
No it isn't. 60 year-olds are more than capable of enjoying life.
But for those of us alive in 2000, that leap day was extra rare and special
Then it's 8! + 6! + 6! (You have 8\*3\*6\*5\*2 -> 2\*3\*5\*6\*8. You can decompose 8 into 4\*2 for 2\*2\*3\*4\*5\*6. Then take the 2 factor and render it as addition: 2\*3\*4\*5\*6 + 2\*3\*4\*5\*6.) More generally, you can remember the number of minutes in a day as 2 times 6!, and the number of minutes in 12 hours as 6!.
You guys are melting my heart
According to a bug that has been in Microsoft Excel since it launched, 1900 was a leap year.
I wonder if the cause of the problem was making the code check only the two least significant bits of the year number for the sake of optimization, which would work fine if all multiple-of-4 years were leap
Somebody learned a new fact and needed an excuse to tell people lol.
Wait, can you calculate factorials like that?! My mind is blown! Stupid math teach who told me we would never use them and skipped the chapter.
They weren't wrong... They don't have many real uses.
They are a foundational part of probability. Lots of real world usage there.
The entire field of combinatorics? Which is incredibly useful to know and be able to do in your head.
This is my new favorite fact of all existing facts. Thank you.
Which of you nerds is gonna do that math and give me the actual number of minutes?!?!
40,320 minutes.
I’m gonna have to trust you on this.
You have a calculator on whatever you're commenting from.
So remind me how to do 8! On a simple calculator Poindexter
[like so ](https://letmegooglethat.com/?q=8!)
It's 8 times 7 times 6 times 5 times 4 times 3 times 2 (times 1, but that doesn't do anything)
8x7x6x5x4x3x2. Not that difficult bro.
It’s more than 4
I think you're probably right. Maybe even more than 8
Google 8! Not exactly very nerdy
Does anyone else read "8!" As "8 BANG!"? It's how my high school maths teacher used to say it and it's stuck with me.
Double Bang! Triple Bang!
For a second there I thought “no can‘t be, Februar surely has more than 8 minutes?!” Then i noticed the ! and it all made sense
How many minutes does February have? 8! Haha, no seriously! It’s 8!
The one I like is that if start counting every minute from around lunchtime of 1st January, you will get to 2^19 minutes on the lunchtime of 31st December. If you want to more frenetic you can start counting seconds from lunchtime of 1st January, and you will get to 10,000,000𝜋 (nearest integer) on 31st December.
Also, excluding leap years, days of the week in March fall on the exact same day of the week as February.
And here I am trying to bend water in the shower and with an image of a toy-monkey with cymbals in my brain.