Go to Post I come to Chief Delphi to get away from the mundane, everyday news. It's part of what makes the forum appealing to me. If I want to read world news, I'll go to digg. - Ryan Dognaux [more]
Home
Go Back   Chief Delphi > Technical > Programming
CD-Media   CD-Spy  
portal register members calendar search Today's Posts Mark Forums Read FAQ rules

 
Closed Thread
Thread Tools Rate Thread Display Modes
  #1   Spotlight this post!  
Unread 14-12-2012, 14:55
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 8,125
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
numerical computation contest


A diversion, for anyone so inclined.


Attached Thumbnails
Click image for larger version

Name:	numer1.png
Views:	414
Size:	12.7 KB
ID:	13287  
  #2   Spotlight this post!  
Unread 14-12-2012, 15:24
Jon Stratis's Avatar
Jon Stratis Jon Stratis is offline
Mentor, LRI, MN RPC
FRC #2177 (The Robettes)
Team Role: Mentor
 
Join Date: Feb 2007
Rookie Year: 2006
Location: Minnesota
Posts: 3,835
Jon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond repute
Re: numerical computation contest

Does the answer have to be completely numerical, or can it contain known variables/equations (for example, could I say pi/8 versus 0.392699..., or 2*sin (1) were either of those the actual answer. Disclaimer: I have done no math at this point, and I highly doubt that I randomly picked the answer )
__________________
2007 - Present: Mentor, 2177 The Robettes
LRI: North Star 2012-2016; Lake Superior 2013-2014; MN State Tournament 2013-2014, 2016; Galileo 2016; Iowa 2017
2015: North Star Regional Volunteer of the Year
2016: Lake Superior WFFA
  #3   Spotlight this post!  
Unread 14-12-2012, 15:25
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 8,125
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: numerical computation contest

Quote:
Originally Posted by Jon Stratis View Post
Does the answer have to be completely numerical, or can it contain known variables/equations (for example, could I say pi/8 versus 0.392699..., or 2*sin (1) were either of those the actual answer. Disclaimer: I have done no math at this point, and I highly doubt that I randomly picked the answer )
Looking for a numerical answer, in decimal form. Winner is person who gets answer correct to the most decimal digits.

edit:
If you can find an exact explicit closed-form analytical solution using only add, subtract, multiply, divide, powers, roots, exponentiation, logarithms, trig functions, and inverse trig functions, you will be declared the winner.


Last edited by Ether : 14-12-2012 at 15:46.
  #4   Spotlight this post!  
Unread 14-12-2012, 15:45
k4mc k4mc is offline
Registered User
AKA: Kushal
FRC #0955 (CV Robotics)
Team Role: Alumni
 
Join Date: Dec 2012
Rookie Year: 2009
Location: Oregon
Posts: 4
k4mc is an unknown quantity at this point
Re: numerical computation contest

I believe the answer is 44.4984550191007992545541 feet

(although I used a "wolfram alpha method" , not an analytic one to solve the equation)
  #5   Spotlight this post!  
Unread 14-12-2012, 15:53
Christopher149 Christopher149 is offline
Registered User
FRC #0857 (Superior Roboworks) FTC 10723 (SnowBots)
Team Role: Mentor
 
Join Date: Jan 2011
Rookie Year: 2007
Location: Houghton, MI
Posts: 1,109
Christopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond repute
Re: numerical computation contest

Is this close?

h = (in ft)
44.49845501910079925455416001673359894996896435222 95612116880595546581686999560519753347236106529250 14422691969000110577445163659978002373921158891281 96107912233956035279094688973264141285038352833979 92808923081071616667853526325563707812597289771290 34979416624799668990733212350734392869697893501318 89111943559177977405431271912121416410363234025409 52753032492871047810149624788135594125012352228840 06058879524106347465534347539833791041297948729285 69084156937833895515653679687331260207084213606326 0

Last edited by Christopher149 : 14-12-2012 at 15:56. Reason: missed a divide by 2
  #6   Spotlight this post!  
Unread 14-12-2012, 16:24
AGPapa's Avatar
AGPapa AGPapa is offline
Registered User
AKA: Antonio Papa
FRC #5895
Team Role: Mentor
 
Join Date: Mar 2012
Rookie Year: 2011
Location: Robbinsville, NJ
Posts: 323
AGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond repute
Re: numerical computation contest

Quote:
Originally Posted by Christopher149 View Post
Is this close?

h = (in ft)
44.49845501910079925455416001673359894996896435222 95612116880595546581686999560519753347236106529250 14422691969000110577445163659978002373921158891281 96107912233956035279094688973264141285038352833979 92808923081071616667853526325563707812597289771290 34979416624799668990733212350734392869697893501318 89111943559177977405431271912121416410363234025409 52753032492871047810149624788135594125012352228840 06058879524106347465534347539833791041297948729285 69084156937833895515653679687331260207084213606326 0
The arc is only one foot longer than the chord. How could the answer possibly be larger than one?

EDIT: Anyway, here is my work. SPOILERS!
/http://i.imgur.com/2IYR8.png

So my guess is zero. It's not exact, but close.

Last edited by AGPapa : 14-12-2012 at 16:37.
  #7   Spotlight this post!  
Unread 14-12-2012, 16:32
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 8,125
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: numerical computation contest

Quote:
Originally Posted by Christopher149 View Post
Is this close?

h = (in ft)
44.49845501910079925455416001673359894996896435222 95612116880595546581686999560519753347236106529250 14422691969000110577445163659978002373921158891281 96107912233956035279094688973264141285038352833979 92808923081071616667853526325563707812597289771290 34979416624799668990733212350734392869697893501318 89111943559177977405431271912121416410363234025409 52753032492871047810149624788135594125012352228840 06058879524106347465534347539833791041297948729285 69084156937833895515653679687331260207084213606326 0
Close enough. Tell the folks how you did it.


  #8   Spotlight this post!  
Unread 14-12-2012, 16:37
Jon Stratis's Avatar
Jon Stratis Jon Stratis is offline
Mentor, LRI, MN RPC
FRC #2177 (The Robettes)
Team Role: Mentor
 
Join Date: Feb 2007
Rookie Year: 2006
Location: Minnesota
Posts: 3,835
Jon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond reputeJon Stratis has a reputation beyond repute
Re: numerical computation contest

Quote:
Originally Posted by AGPapa View Post
The arc is only one foot longer than the chord. How could the answer possibly be larger than one?
Create a simple approximation. Imagine a point C that lies at the top of the line H. You can then create a triangle ABC, where length AB is known (5280 ft) and length BC = AC = 5281/2 = 2640.5.

We know that h bisects line AB - lets call the intersection between AB and h to be H. we know that the length AH = BH = 5280/2 = 2640.

So, now we know two sides to the right triangle AHC - AH and AC. Taking the square of the hypotenuse minus the square of one side gives us the square of the other side. In other words, 2640.5^2 - 2640^2 = h^2 (the pythagorean theorem).

So, in this extremely rough approximation, we get h = 51.383. Given that, it's not hard to imagine that Christopher's answer could be correct, to some number of decimal places.
__________________
2007 - Present: Mentor, 2177 The Robettes
LRI: North Star 2012-2016; Lake Superior 2013-2014; MN State Tournament 2013-2014, 2016; Galileo 2016; Iowa 2017
2015: North Star Regional Volunteer of the Year
2016: Lake Superior WFFA
  #9   Spotlight this post!  
Unread 14-12-2012, 16:48
AGPapa's Avatar
AGPapa AGPapa is offline
Registered User
AKA: Antonio Papa
FRC #5895
Team Role: Mentor
 
Join Date: Mar 2012
Rookie Year: 2011
Location: Robbinsville, NJ
Posts: 323
AGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond reputeAGPapa has a reputation beyond repute
Re: numerical computation contest

Quote:
Originally Posted by Jon Stratis View Post
Create a simple approximation. Imagine a point C that lies at the top of the line H. You can then create a triangle ABC, where length AB is known (5280 ft) and length BC = AC = 5281/2 = 2640.5.

We know that h bisects line AB - lets call the intersection between AB and h to be H. we know that the length AH = BH = 5280/2 = 2640.

So, now we know two sides to the right triangle AHC - AH and AC. Taking the square of the hypotenuse minus the square of one side gives us the square of the other side. In other words, 2640.5^2 - 2640^2 = h^2 (the pythagorean theorem).

So, in this extremely rough approximation, we get h = 51.383. Given that, it's not hard to imagine that Christopher's answer could be correct, to some number of decimal places.
Thanks!
  #10   Spotlight this post!  
Unread 14-12-2012, 16:51
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 8,125
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: numerical computation contest

Quote:
Originally Posted by Jon Stratis View Post
it's not hard to imagine that Christopher's answer could be correct, to some number of decimal places.
498 decimal places

I checked them. They appear to be correct.


  #11   Spotlight this post!  
Unread 14-12-2012, 16:56
Christopher149 Christopher149 is offline
Registered User
FRC #0857 (Superior Roboworks) FTC 10723 (SnowBots)
Team Role: Mentor
 
Join Date: Jan 2011
Rookie Year: 2007
Location: Houghton, MI
Posts: 1,109
Christopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond repute
Re: numerical computation contest

Quote:
Originally Posted by Ether View Post
Close enough. Tell the folks how you did it.


Since this is a circular arc, I start with a circle. Based off of a diagram like this, I draw a triangle and take theta to be as is shown in that picture. From the right triangle, we know radius * sin(theta) = 5280 / 2. From the definition of arc length, we also know that radius * 2 * theta = 5281. We have two equations and two unknowns, so I substituted one into the other and let Mathematica determine theta. From theta, we easily get the radius. Next, we use this equation relating chord length and the height to the radius. Again, I let Mathematica handle the equation to a ridiculous number of decimal places.

Mathematica Code
Code:
Clear[t, h, r, c, a]
c = 5280
a = 5281
t = t /. 
  FindRoot[a/(2 t) * Sin[t] == c/2, {t, 1.8}, 
   AccuracyGoal -> 100000, PrecisionGoal -> 100000, 
   WorkingPrecision -> 500]
r = a/(2 t)
FindRoot[r == c^2/(8 h) + h/2, {h, 100}, AccuracyGoal -> 100000, 
 PrecisionGoal -> 100000, WorkingPrecision -> 500]
EDIT: I can get more decimal places ...

Last edited by Christopher149 : 14-12-2012 at 16:57. Reason: partial reply to post that beat mine
  #12   Spotlight this post!  
Unread 14-12-2012, 16:57
BigJ BigJ is offline
Registered User
AKA: Josh P.
FRC #1675 (Ultimate Protection Squad)
Team Role: Engineer
 
Join Date: Jan 2007
Rookie Year: 2007
Location: Milwaukee, WI
Posts: 947
BigJ has a reputation beyond reputeBigJ has a reputation beyond reputeBigJ has a reputation beyond reputeBigJ has a reputation beyond reputeBigJ has a reputation beyond reputeBigJ has a reputation beyond reputeBigJ has a reputation beyond reputeBigJ has a reputation beyond reputeBigJ has a reputation beyond reputeBigJ has a reputation beyond reputeBigJ has a reputation beyond repute
Re: numerical computation contest

I was bored and tried to find a closed form by hand, it didn't work out by the time I refreshed it and it was over

  #13   Spotlight this post!  
Unread 14-12-2012, 17:16
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 8,125
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: numerical computation contest

Quote:
Originally Posted by Christopher149 View Post
Mathematica Code
Code:
Clear[t, h, r, c, a]
c = 5280
a = 5281
t = t /. 
  FindRoot[a/(2 t) * Sin[t] == c/2, {t, 1.8}, 
   AccuracyGoal -> 100000, PrecisionGoal -> 100000, 
   WorkingPrecision -> 500]
r = a/(2 t)
FindRoot[r == c^2/(8 h) + h/2, {h, 100}, AccuracyGoal -> 100000, 
 PrecisionGoal -> 100000, WorkingPrecision -> 500]
Here's Maxima code:
Code:
fpprec: 600$
L:5280$ eps:1$
y: x/sin(x)-(L+eps)/L$
a: bf_find_root(y,x,1/1000,4/100);
h: (L/2)*(1-cos(a))/sin(a);
Quote:
EDIT: I can get more decimal places ...
So can I
Code:
Maxima 5.27.0 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.

(%i1) fpprec: 600$
L:5280$ eps:1$
y: x/sin(x)-(L+eps)/L$
a: bf_find_root(y,x,1/1000,4/100);
h: (L/2)*(1-cos(a))/sin(a);

4.4498455019100799254554160016733598949968964352229561211688059554658168\
699956051975334723610652925014422691969000110577445163659978002373921158891281\
961079122339560352790946889732641412850383528339799280892308107161666785352632\
556370781259728977129034979416624799668990733212350734392869697893501318891119\
435591779774054312719121214164103632340254095275303249287104781014962478813559\
412501235222884006058879524106347465534347539833791041297948729285690841569378\
338955156536796873312602070842136063260258182278201500825791387457906343098887\
9258590281352783951539842610751922916884732140489864979154825b1
(%i7)
  #14   Spotlight this post!  
Unread 14-12-2012, 17:28
Christopher149 Christopher149 is offline
Registered User
FRC #0857 (Superior Roboworks) FTC 10723 (SnowBots)
Team Role: Mentor
 
Join Date: Jan 2011
Rookie Year: 2007
Location: Houghton, MI
Posts: 1,109
Christopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond reputeChristopher149 has a reputation beyond repute
Post Re: numerical computation contest

Quote:
Originally Posted by Ether View Post
Code:
4.4498455019100799254554160016733598949968964352229561211688059554658168\
699956051975334723610652925014422691969000110577445163659978002373921158891281\
961079122339560352790946889732641412850383528339799280892308107161666785352632\
556370781259728977129034979416624799668990733212350734392869697893501318891119\
435591779774054312719121214164103632340254095275303249287104781014962478813559\
412501235222884006058879524106347465534347539833791041297948729285690841569378\
338955156536796873312602070842136063260258182278201500825791387457906343098887\
9258590281352783951539842610751922916884732140489864979154825b1
(%i7)
4.4498 ... I thought it was 44.498 ...
  #15   Spotlight this post!  
Unread 14-12-2012, 17:53
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 8,125
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: numerical computation contest

Quote:
Originally Posted by Christopher149 View Post
4.4498 ... I thought it was 44.498 ...
Um... The exponent is at the end of those 600 digits


Closed Thread


Thread Tools
Display Modes Rate This Thread
Rate This Thread:

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump


All times are GMT -5. The time now is 02:26.

The Chief Delphi Forums are sponsored by Innovation First International, Inc.


Powered by vBulletin® Version 3.6.4
Copyright ©2000 - 2017, Jelsoft Enterprises Ltd.
Copyright © Chief Delphi