File:Close-packed spheres, with umbrella light & camerea.jpg

Technopedia Center

Faculty of Engineering and Computer Science
S1 Informatics S1 Information Systems S1 Information Technology S1 Computer Engineering S1 Electrical Engineering S1 Civil Engineering

faculty of Economics and Business
S1 Management S1 Accountancy

Faculty of Letters and Educational Sciences
S1 English literature S1 English language education S1 Mathematics education S1 Sports Education

File:Close-packed spheres, with umbrella light & camerea.jpg - Wikipedia

From Wikipedia, the free encyclopedia

Size of this preview: 623 × 599 pixels. Other resolutions: 249 × 240 pixels | 499 × 480 pixels | 798 × 768 pixels | 1,064 × 1,024 pixels | 1,500 × 1,443 pixels.

Original file (1,500 × 1,443 pixels, file size: 374 KB, MIME type: image/jpeg)

This is a file from the Wikimedia Commons. Information from its description page there is shown below.
Commons is a freely licensed media file repository. You can help.

Summary

Description	English: The cannonball stack: an “FCC” latice.
Date	8 February 2011
Source	English Wikipedia
Author	Greg A L

Shown above is what the science of sphere packing calls a closest-packed arrangement. Specifically, this is the cannonball arrangement or cannonball stack. Thomas Harriot in ca. 1585 first pondered the mathematics of cannonball stacks and later asked Johannes Kepler if the stack illustrated here was truly the most efficient. Kepler wrote, in what today is known as the Kepler conjecture, that no other arrangement of spheres can exceed its packing density of 74%.^[1]

Mathematically, there is an infinite quantity of closest-packed arrangements (assuming an infinite-size volume in which to arrange spheres). In the field of crystal structure however, unit cells (a crystal’s repeating pattern) are composed of a limited number of atoms and this reduces the variety of closest-packed regular lattices found in nature to only two: hexagonal close packed (HCP), and face-centered cubic (FCC). As can be seen at this site at King’s College, there is a distinct, real difference between different lattices; it’s not just a matter of how one slices 3D space. With all closest-packed lattices however, any given internal atom is in contact with 12 neighbors — the maximum possible.

Note that this stack is not a FCC unit cell since this group can not tessellate in 3D space. Visit the King’s College Web site to see HCP and FCC unit cells.

When many chemical elements (such as most of the noble gases and platinum-group metals) freeze solid, their lattice unit cells are of the FCC form. Having a closest-packed arrangement is one of the reasons why iridium and osmium (both of which are platinum-group metals) have the two greatest bulk densities of all the chemical elements.

The stack shown here is indeed quite dense. If this stack of 35 spheres was composed of iron cannonballs, each measuring 10 cm in diameter, the top of the stack would be only 42.66 cm off the ground — just under the knee of the average barefoot man — and yet would weigh over 144 kg.

↑ To 23 significant digits, the value is 74.048 048 969 306 104 116 931%

Rendered and modeled using Cobalt CAD package.

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

You are free:

to share – to copy, distribute and transmit the work
to remix – to adapt the work

Under the following conditions:

attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.

You may select the license of your choice.

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
current	01:07, 9 February 2011		1,500 × 1,443 (374 KB)	Greg A L	{{Information \|Description ={{en\|1=The cannonball stack: an “FCC” latice.}} \|Source ={{own}} \|Author =Greg A L \|Date =2011-02-08 \|Permission = \|other_versions =File:Close-packed spheres.jpg }}

File usage

The following 3 pages use this file:

Global file usage

The following other wikis use this file:

Usage on pt.teknopedia.teknokrat.ac.id
- Empacotamento compacto de esferas iguais
Usage on ru.teknopedia.teknokrat.ac.id
- Плотная упаковка равных сфер
Usage on uk.wikipedia.org
- Щільне пакування рівних сфер

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Width	3,000 px
Height	2,885 px
Compression scheme	Uncompressed
Pixel composition	RGB
Orientation	Normal
Number of components	3
Horizontal resolution	72 dpi
Vertical resolution	72 dpi
Data arrangement	chunky format
Software used	Adobe Photoshop CS2 Macintosh
File change date and time	17:04, 8 February 2011
Color space	Uncalibrated

Summary

Licensing

Captions

Items portrayed in this file

depicts

copyright status

copyrighted

copyright license

GNU Free Documentation License, version 1.2 or later

Creative Commons Attribution-ShareAlike 3.0 Unported

inception

8 February 2011

source of file

original creation by uploader

media type

image/jpeg

checksum

91952ccf0a78c8df2b5c9356d58e671dd193041b

data size

382,594 byte

height

1,443 pixel

width

1,500 pixel

File history

File usage

Global file usage

Metadata