My Math Forum  

Go Back   My Math Forum > High School Math Forum > Trigonometry

Trigonometry Trigonometry Math Forum

LinkBack Thread Tools Display Modes
April 8th, 2017, 01:05 AM   #1
Joined: Apr 2017
From: England

Posts: 1
Thanks: 0

Off-Centre Sphere Stacking. Trigonometry

Dear My Math Forum,

I have been trying to figure out how to find the position(height) of spheres on a 2nd layer above a 1st layer of HCP Spheres. The 2nd layer are offset from the 'deep hole' of the 1st layers 3 spheres. They do not sit in the centre.

I have attached an image to show the positions. I want to work out the 'white x' height of the 2nd layer

If I place a sphere at 0,0,0 (centred in the image) the 'x' or 'y' positions of the layer 1 spheres are
'y' = -.5,
'x' = 0.866 025 403 784 438 646 763 723 170 752 936 183 471 402 63,
'z' = 0

Doubling this number gives me the further sphere positions of layer 1.

Layer 2's spheres are positioned by swopping the 'x' and 'y', still using the 0.866025 number.

What is the height of the 2nd layer. The Spheres are '1' diameter
Attached Images
File Type: jpg off centre stacking.jpg (27.8 KB, 0 views)
File Type: jpg layer 1-2 overlapped.jpg (48.1 KB, 0 views)
File Type: jpg hcp layer 2.jpg (33.1 KB, 0 views)

Last edited by Slaterdom; April 8th, 2017 at 01:11 AM.
Slaterdom is offline  

  My Math Forum > High School Math Forum > Trigonometry

offcentre, sphere, stacking, trigonometry

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
centre circle in 3D andreaugust Algebra 2 October 28th, 2013 09:29 AM
Cluster centre problem felicia184 Algebra 5 September 17th, 2012 06:16 PM
Centre of mass arron1990 Calculus 2 September 12th, 2012 08:49 AM
Centre Fernando Abstract Algebra 2 April 30th, 2012 03:41 PM
Centre and the radius of a circle squeeze101 Algebra 3 November 21st, 2008 07:37 PM

Copyright © 2017 My Math Forum. All rights reserved.