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

Home > Shapes > Geometry
Pentagonal triple triangles (Posted on 2016-07-01) Difficulty: 3 of 5
Which triangular numbers are three times a pentagonal number?

Is there a geometrical interpretation to this?

No Solution Yet Submitted by Jer    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: computer method (the part that wouldn't fit) | Comment 3 of 4 |
(In reply to computer method by Charlie)

 
 The kth triangular number is 3 times a pentagonal number if k = 2 mod 3.
 
 DefDbl A-Z
 Dim crlf$
 
 
 Private Sub Form_Load()
  Form1.Visible = True
  
  
  Text1.Text = ""
  crlf = Chr$(13) + Chr$(10)
  
  For n = 1 To 1000
   DoEvents
   p = (3 * n * n - n) / 2
   tr = 3 * p
   Text1.Text = Text1.Text & mform(n, "####0") & mform(p, "#########0") & mform(p * 3, "#########0") & mform(isTri(tr), "######0") & crlf
  Next
  
  
  Text1.Text = Text1.Text & crlf & " done"
   
 End Sub
 
 Function isTri(t)
 n = Int(Sqr(t * 2))
 np = n + 1
 If n * np = 2 * t Then isTri = n Else isTri = 0
 End Function
 
 Function mform$(x, t$)
   a$ = Format$(x, t$)
   If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
   mform$ = a$
 End Function
 


  Posted by Charlie on 2016-07-01 10:14:21
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 (3)
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