All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Phibobrick's dimensions (Posted on 2016-10-14) Difficulty: 3 of 5
Imagine a brick with sides of lengths 1, Phi=1·61803... and phi=1/Phi=0·61803.

Clearly, the longest side is the sum of the other two lengths since 1 + phi = Phi

i. Show that the largest face (area C=1 x Phi) is the sum of the other two face's areas (area A =1 x phi and area B=phi x Phi) ?
ii. Evaluate the surface area S of the brick.
iii. Find the diagonal across the brick.
iv. What is the ratio of the surface areas of the "Phi-bonacci brick" and its surrounding sphere?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution proposed solution Comment 1 of 1
i. A = 1*phi = 1/Phi; B = phi*Phi = 1

 Phi = phi + 1
 1 * Phi = 1*phi + phi*Phi
 C = A + B
 
ii. S = 2*(phi + Phi + 1) = 4 * Phi = 2*(1 + sqrt(5))

iii. Phi^2 = 1+Phi
     phi^2 = 2-Phi
     
     d^2 = 1 + Phi^2 + phi^2
         = 1 + 3 
         = 4
         
     d = 2
     
iv.  r = d/2 = 1
     A = 4 * pi 
     
     S/A = (1+sqrt(5))/(2*pi) = Phi/pi ~= .5150362148004845


  Posted by Charlie on 2016-10-14 11:45:47
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information