Zelaron Gaming Forum  
Stats Arcade Portal Forum FAQ Members List Social Groups Calendar Search Today's Posts Mark Forums Read
Go Back   Zelaron Gaming Forum > The Zelaron Nexus > Science and Art > Science and Technology News

 
 
Thread Tools Display Modes

 
High school geometry problem finally solved after 272 years
Reply
Posted 2020-12-13, 07:45 AM


Question: How big must r be chosen in the diagram, in order for the red area to equal one half of the area of the circle?

The above problem was first posed in 1748, and it has been known since then that r is approximately equal to 1.1578. Apparently it just took us 272 years to figure out an exact solution to it. Namely,



where the integrals are contour integrals.

Good job, humanity.

In all seriousness, it's fascinating how difficult trivial-looking math problems can become once you start to experiment a little with the functions/constants/boundary conditions/shapes/etc. Another good example of this is the calculation of the arc length of a curve.

Specifically, if y = f(x) is a continuously differentiable function on the interval (a,b), then its arc length s between a and b is



There are some simple exact solutions to the above integral, but let's just say that there are reasons why most calculus textbooks stick to examples where f(x) describes either a line, parabola, circle or hyperbolic cosine curve...

https://en.wikipedia.org/wiki/Arc_length
Quote:
In most cases, including even simple curves, there are no closed-form solutions for arc length and numerical integration is necessary.
"Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram

Last edited by Chruser; 2020-12-13 at 08:11 AM.
Old
Profile PM WWW Search
Chruser shouldn't have fed itChruser shouldn't have fed itChruser shouldn't have fed itChruser shouldn't have fed itChruser shouldn't have fed it
 
 
Chruser
 
 

Bookmarks

« Previous Thread | Next Thread »

Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)
 
Thread Tools
Display Modes

Posting Rules [Forum Rules]
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts
BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
My first goals... -Spector- Life Discussion 5 2009-03-31 03:35 PM
Three states eye bold high school reforms KagomJack News and Events 1 2008-11-14 04:03 PM
Life simulator Penguin General Discussion 26 2004-07-21 07:25 PM
School Acer The Lounge 41 2003-08-15 06:44 PM


All times are GMT -6. The time now is 03:42 PM.
'Synthesis 2' vBulletin 3.x styles and 'x79' derivative
by WetWired the Unbound and Chruser
Copyright ©2002-2008 zelaron.com
Powered by vBulletin® Version 3.8.2
Copyright ©2000 - 2024, Jelsoft Enterprises Ltd.
This site is best seen with your eyes open.