473,725 Members | 1,987 Online
Bytes | Software Development & Data Engineering Community
+ Post

Home Posts Topics Members FAQ

Tiling and Spacefilling

[ slightly improved over Math Forum draft ]

Probably a fault line or cultural divide between acutely
differing schools of thought, is in this area of tiling
or mosaic making. Some schools consider this a stupid
waste of time, others a core topic, whereas a 3rd group
stays more neutral on the issue, and a tiny 4th group has
no idea what I'm talking about.

I'm in the second group (core topic) as tiling is to
spacefilling as figurate are to polyhedral numbers.
We may start in a plane, in deference to some millenia
of pre-NASA reflex conditioning, but we're still on a
runway, accelerating, and before long (way sooner than
in traditional curricula), we'll be airborne, moving
up into higher D. Tetrahedra are most definitely a
feature of K-5. If NCTM doesn't grasp that, it's
missing the boat.

Back to tiling: we have the classifications , the Escher
lithographs (which follow into Part Two), and the tie ins
to Mesopotamian religions, the three biggies especially,
and their respective sacred geometries. I know "sacred
geometry" is taboo in traditional mathematics, but this
is ~M!, Katrina Network type stuff, closer to George Bush
Sr.'s "voodoo economics" (except managed more by geeks
(Bush was more of a jock, not that we can't share power)).

Rolling forward, we get to the Kepler-Penrose aperiodic
tiling studies, various heuristics, again finding echoes
in Part Two (in what some Russians call stereometry),
where we likely look at Hargittai & Hargittai (Hungarian),
plus Chakovian coordinates (quadrays, simplicials,
whatever nomenclature).

I've already made the case for Polyhedra numerous times.
Thanks to breakthroughs in architecture in the 20th
century, we're obligated to teach about the hexapent in
some way shape or form. Katrina Network is strong on
this, but you'll find other sources. Top of my list
would be J. Baldwin's 'Bucky Works' (packed with ~M!).

For a more prefrequency approach, I recommend Cromwell's
'Polyhedra', and its cartoon proof of Euler's V + F =
E + 2 based on the interdigitating trees of Von Staudt's.

And of course we're not about to bleep over Fuller's
volumes tables, nor MITEs, nor the Jitterbug Trans-
formation -- all pure gold as far as we're concerned.

So to recap... Given I'm of a school which regards
tiling as core, I'm putting my shoulder behind two big
initiatives in computer science these days: CP4E and
HP4E.

CP4E was hatched by Guido, BDFL of Python Nation, and
DARPA, and carried forward billiantly (at least one
doctoral dissertation already on file, about our early
beginnings as a think tank slash on-line community [1]).

HP4E was hatched by yours trully, though mostly as a
marketing gimmick in homage to CP4E and Wanderer Glenn
Stockton's global matrix campaign. I certainly take
advantage of Python a lot, using its generators (a recent
feature) to spit out successive terms in figurate and
polyhedral number sequences, e.g. 1, 3, 6, 10... and
1, 12, 42, 92... (see my Focal Points for more details,
plus my CP4E website, one of many curriculum "hot springs"
in our cyberspace-based Python Nation [2][3]).

Kirby

[1] John Miller's PhD dissertation, Promoting Computer
Literacy Through Programming Python (1.37 MB), looks at
the issues around teaching with Python, and explores some
of the threads taken up on edu-sig.
http://www.python.org/community/sigs/current/edu-sig/

[2] Focal Points:
http://mybizmo.blogspot.com/2006/09/focal-points.html

[3] CP4E website: http://www.4dsolutions.net/ocn/cp4e.html

===

For more on ~M!:
http://worldgame.blogspot.com/2007/01/m.html

Jan 18 '07 #1
0 1242

This thread has been closed and replies have been disabled. Please start a new discussion.

Similar topics

1
3755
by: Derek Fountain | last post by:
I have an image which I want to tile in a table cell. The table cell should expand to fill "the rest of the width" available. This works in Mozilla: <td width="100%" background="images/topbar_05.gif">&nbsp;</td> But the background attribute isn't actually valid in the td tag. For that reason Konqueror doesn't support it, and that's one of the browsers I must have. Is there an alternative way?
0
1085
by: Jim Hubbard | last post by:
By true tiling I do not mean the Vertical tiling or horizontal tiling like .... 1 2 3 4 or
8
3770
by: Ron Holmes | last post by:
I want to place a background image on a windows form. Is there a way to prevent the image from Tiling without using an image box resized to the size of the form? I am using Visual Studio 2003 .NET. This is an easy thing to do in VB6.
16
2649
by: WindAndWaves | last post by:
Hi everyone, I have a main menu that opens a report and a form that I would like to display at the same time (while hiding the main menu). So far, I made the form a pop-up and the report a preview so that both are visible. The form is really small so it works. However, it would be much better if I could tile the report and the form vertically where the form takes up about 5cm and the report the rest of the
1
954
by: Jim Hubbard | last post by:
By true tiling I don't mean the vertical or horizontal tiling that is normally though of like... 123 or 1 2 3
3
9392
by: Sridhar | last post by:
Hi, I have created a user control which has the html code as follows <TABLE id="ToolBarTable" cellSpacing="0" cellPadding="0" width="100%" border="0"> <tr> <td align="right" bgColor="#000000"><IMG src="../Images/image1"> </td> </tr> <TR>
3
3240
by: Viken Karaguesian | last post by:
Hello all, I need somehelp with background tiling. I have a sneaking suspicion that what I want to do is not possible, but I'll ask anyway. :>) First some background: Here's the site in question: www.sayatnova.com (I'm sure many of you have seen this before as I've often asked for help). I've come a long way since I first created the site many moons ago and I'm trying to convert it to a (1) Table-less, (2) Frame-less and (3) Validated...
0
8886
marktang
by: marktang | last post by:
ONU (Optical Network Unit) is one of the key components for providing high-speed Internet services. Its primary function is to act as an endpoint device located at the user's premises. However, people are often confused as to whether an ONU can Work As a Router. In this blog post, we’ll explore What is ONU, What Is Router, ONU & Router’s main usage, and What is the difference between ONU and Router. Let’s take a closer look ! Part I. Meaning of...
0
8750
by: Hystou | last post by:
Most computers default to English, but sometimes we require a different language, especially when relocating. Forgot to request a specific language before your computer shipped? No problem! You can effortlessly switch the default language on Windows 10 without reinstalling. I'll walk you through it. First, let's disable language synchronization. With a Microsoft account, language settings sync across devices. To prevent any complications,...
0
9255
jinu1996
by: jinu1996 | last post by:
In today's digital age, having a compelling online presence is paramount for businesses aiming to thrive in a competitive landscape. At the heart of this digital strategy lies an intricately woven tapestry of website design and digital marketing. It's not merely about having a website; it's about crafting an immersive digital experience that captivates audiences and drives business growth. The Art of Business Website Design Your website is...
1
9168
by: Hystou | last post by:
Overview: Windows 11 and 10 have less user interface control over operating system update behaviour than previous versions of Windows. In Windows 11 and 10, there is no way to turn off the Windows Update option using the Control Panel or Settings app; it automatically checks for updates and installs any it finds, whether you like it or not. For most users, this new feature is actually very convenient. If you want to control the update process,...
0
9104
tracyyun
by: tracyyun | last post by:
Dear forum friends, With the development of smart home technology, a variety of wireless communication protocols have appeared on the market, such as Zigbee, Z-Wave, Wi-Fi, Bluetooth, etc. Each protocol has its own unique characteristics and advantages, but as a user who is planning to build a smart home system, I am a bit confused by the choice of these technologies. I'm particularly interested in Zigbee because I've heard it does some...
1
6701
isladogs
by: isladogs | last post by:
The next Access Europe User Group meeting will be on Wednesday 1 May 2024 starting at 18:00 UK time (6PM UTC+1) and finishing by 19:30 (7.30PM). In this session, we are pleased to welcome a new presenter, Adolph Dupré who will be discussing some powerful techniques for using class modules. He will explain when you may want to use classes instead of User Defined Types (UDT). For example, to manage the data in unbound forms. Adolph will...
0
4780
by: adsilva | last post by:
A Windows Forms form does not have the event Unload, like VB6. What one acts like?
1
3217
by: 6302768590 | last post by:
Hai team i want code for transfer the data from one system to another through IP address by using C# our system has to for every 5mins then we have to update the data what the data is updated we have to send another system
2
2632
muto222
by: muto222 | last post by:
How can i add a mobile payment intergratation into php mysql website.

By using Bytes.com and it's services, you agree to our Privacy Policy and Terms of Use.

To disable or enable advertisements and analytics tracking please visit the manage ads & tracking page.