FAQ
It is currently Sat Sep 23, 2017 5:41 am


Author Message
Peter Dow
Post  Post subject: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Fri Nov 18, 2016 5:50 pm
User avatar

Joined: Wed May 28, 2014 11:58 pm
Posts: 9
Location: Aberdeen, Scotland

Offline
I'm going to try for the "Mathematics" forum for this topic but no worries if the mods decide to move this to "Art and Culture".

I've posted this image which I've described as a
"Three-spoke dovetailing tile tessellation".

URL REMOVEDImage
URL REMOVED, on Flickr

which is a tessellation of this tile shape,
URL REMOVEDImage
URL REMOVED, on Flickr

Check my Flickr page for the preceding design iterations and inspiration.

I've named the shape
Trispokedovetile
which is a contraction of "tri-spoke dovetailing tile".
  • "tri-spoke" because the shape is similar to a 3-spoke motorcycle wheel with three bites taken out of it.
  • "dovetailing" because the tiles interlock like a dovetail joint

But it is quite possible this shape is already known to geometry and already has been named.

Do you know if this shape has already been named? If so please do reply to tell me what the name is.


Top
Peter Dow
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Sat Nov 19, 2016 10:44 pm
User avatar

Joined: Wed May 28, 2014 11:58 pm
Posts: 9
Location: Aberdeen, Scotland

Offline
Trispokedovetiles Animation Webpage [LINK]
 
I've programmed a webpage using Javascript to display an animation which shows a range of different trispokedovetiles, each of which can be specified by a "CIRCLE" percentage, which is the ratio as a percent of two parameters -
 
1. A "HEXAGON" parameter length - always nominally "100%"
2. A "CIRCLE" parameter length - the animation varies this between 100% and 135%, though up to 150% is possible in theory.
 
So you can specify the "CIRCLE" percentage to specify a particular shape of trispokedovetile.
 
Here is a still image from the animation - showing the trispokedovetiles with "CIRCLE" = 125%.

Image
by Peter Dow, on Flickr
 
I've tested the animation in Chrome and Internet Explorer browsers and it works fine for me.
 
But it is not working in Firefox for some as yet unknown reason.
 
Let me know by replying here if you have any other problems with the animation not displaying for you.


Top
iNow
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Sun Nov 20, 2016 12:13 am
User avatar
Original Member
Original Member

Joined: Thu Aug 04, 2011 11:40 pm
Posts: 5700
Location: Iowa

Offline
All of your spammy links have (again) been deleted

_________________
iNow

"[Time] is one of those concepts that is profoundly resistant to a simple definition." ~C. Sagan


Top
Peter Dow
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Wed Nov 23, 2016 12:30 pm
User avatar

Joined: Wed May 28, 2014 11:58 pm
Posts: 9
Location: Aberdeen, Scotland

Offline
Image
A trispokedovetile in 3D

Image
3 trispokedovetiles in 3D


Top
paleoichneum
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Wed Nov 23, 2016 3:30 pm
User avatar
Original Member
Original Member

Joined: Fri Aug 05, 2011 1:23 am
Posts: 507

Offline
Peter, what is your point? (Other then discovering M. C. Esher imagery?)

_________________
The needs of the many outweigh the need of the few - Spock of Vulcan & Sentinel Prime of Cybertron ---proof that "the needs" are in the eye of the beholder.


Top
Peter Dow
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Wed Nov 23, 2016 6:42 pm
User avatar

Joined: Wed May 28, 2014 11:58 pm
Posts: 9
Location: Aberdeen, Scotland

Offline
paleoichneum wrote:
Peter, what is your point? (Other then discovering M. C. Esher imagery?)

My first point is a mathematical science point - to specify and to demonstrate a class of geometric shapes apparently heretofore not specified mathematically and only known about by artists in the sense that they have approximated these shapes in artistic tessellations.

It would help my demonstration here if the mod would allow me to post at least one link
LINK REMOVED
to my trispokedovetiles webpage, rather than deleting all links regardless of relevance.

My second point is an engineering science point - this class of geometric shapes have possible engineering applications.

Possible application to tiled armour

One issue with hexagonal or square armour tiles is that such simple shapes don't interlock sideways, as do jigsaw puzzle pieces.

Whilst a little armour tile movement in the same direction as the bullet (normal to the armour plane) is useful in absorbing the kinetic energy of the bullet (and much better than the armour tile absorbing the same kinetic energy by shattering), on the other hand, sideways tile movement (tangential to the armour plane) leaves most unwelcome gaps in the armour in between separated tiles.

So armour tiles shaped like jigsaw puzzle shapes (or some hexagonal variation such as these trispokedovetiles) could perform well in this application.


Top
iNow
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Wed Nov 23, 2016 8:51 pm
User avatar
Original Member
Original Member

Joined: Thu Aug 04, 2011 11:40 pm
Posts: 5700
Location: Iowa

Offline
Peter Dow wrote:
It would help my demonstration here if the mod would allow me to post at least one link LINK REMOVED to my trispokedovetiles webpage, rather than deleting all links regardless of relevance.

Demonstrate the relevance then, and I'll consider leaving the link.

At this point, and even after reading this post in response to someone asking about relevance, that relevance remains unclear.

Specifically: What do you wish to discuss? What questions do you wish to explore with this community?

Start there, and have your discussion here. You won't be allowed to drive traffic to your site using ours as a vehicle. Thank you for your understanding.

_________________
iNow

"[Time] is one of those concepts that is profoundly resistant to a simple definition." ~C. Sagan


Top
Peter Dow
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Tue Nov 29, 2016 4:56 pm
User avatar

Joined: Wed May 28, 2014 11:58 pm
Posts: 9
Location: Aberdeen, Scotland

Offline
Now to consider the important issue of interlocking trispokedovetiles against movement in the direction normal to the tiled plane, which for the application of tiled armour would be the normal to the armour surface, in the direction of a bullet's path.

BILAYER TRISPOKEDOVETILES

I propose that the unit armour tile be comprised of 2 joined trispokedovetiles with matching HEXAGON parameters but each with a different CIRCLE percentage.

For example, suppose we choose trispokedovetiles with CIRCLE = 100% and 121%.

Image Image

The reason for choosing C100 for the outer layer of the armour is because its 120 angle corners would be more robust.

The reason for choosing C121 for the inner layer of the armour is because CIRCLE = 121% offers the largest percentage where the neck attacking the outer part rings is at least twice the thickness of the ring, attempting to balance the robustness of the ring parts to the robustness of the neck versus tensile stresses.

Image

Stacking and joining those together forms a bilayer trispokedovetile, "C100+C121".

Image Image

Drawing the 2 layers semi-transparently we can see how the bilayer trispokedovetiles would interlock in the normal to the plane.

Image

2/3rds of the tiles can be slotted together, either the yellows and the blues or the yellows and the purples or the blues and the purples.

However the final 1/3rd of the tiles would not simply slot in and would have be inserted by joining the two halves of the bilayer trispokedovetile in situ.


Top
paleoichneum
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Tue Nov 29, 2016 5:20 pm
User avatar
Original Member
Original Member

Joined: Fri Aug 05, 2011 1:23 am
Posts: 507

Offline
With all the text you posted, there is no demonstration of increased benefit to the use of your structuring. And it looks more rigid then current armour structures

_________________
The needs of the many outweigh the need of the few - Spock of Vulcan & Sentinel Prime of Cybertron ---proof that "the needs" are in the eye of the beholder.


Top
wireless
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Thu Dec 08, 2016 8:28 pm

Joined: Mon Aug 15, 2011 9:55 am
Posts: 291

Offline
For what it is worth, I thought that Peter Dow was a political activist. There may be some obscure mathematical/political stuff going on with the OP. Peter Dow is a very interesting person.
http://peter-dow.blogspot.co.uk/


Top
marnixR
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Thu Dec 08, 2016 8:30 pm
User avatar

Joined: Thu Aug 04, 2011 8:35 pm
Posts: 4848
Location: Cardiff, Wales

Offline
definitely one and the same ?

_________________
"Reality is that which, when you stop believing in it, doesn't go away." (Philip K. Dick)
"Someone is WRONG on the internet" (xkcd)


Top
Peter Dow
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Thu Dec 08, 2016 8:43 pm
User avatar

Joined: Wed May 28, 2014 11:58 pm
Posts: 9
Location: Aberdeen, Scotland

Offline
For Computer-Aided Manufacturing of trispokedovetiles, I've published a Javascript web-page -
(Google -)
"Trispokedovetiles: CNC code to cut tiles"
(and you may find my post on a cnc forum with a link to my page - sorry for the run around but as you probably have noted I am not allowed to post links here)
- which generates Computer Numerical Control (CNC) code which I've tested with CNC Simulator Pro but not on a real CNC cutter as yet.


Top
PhDemon
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Thu Dec 08, 2016 8:51 pm

Joined: Wed Jun 26, 2013 10:44 am
Posts: 499
Location: Newcastle-upon-Tyne

Offline
Quote:
Peter Dow is a very interesting person.


If it is the same guy the page about him on rationalwiki is very funny (and a bit disturbing)... ;)

_________________
"The big trouble with dumb bastards is that they are too dumb to believe there is such a thing as being smart"

- Kurt Vonnegut, The Sirens of Titan


Top
paleoichneum
Post  Post subject: Re: Geometry. Three-spoke dovetailing tile tessellation.  |  Posted: Tue Dec 13, 2016 8:42 pm
User avatar
Original Member
Original Member

Joined: Fri Aug 05, 2011 1:23 am
Posts: 507

Offline
Peter Dow wrote:
For Computer-Aided Manufacturing of trispokedovetiles, I've published a Javascript web-page -
(Google -)
"Trispokedovetiles: CNC code to cut tiles"
(and you may find my post on a cnc forum with a link to my page - sorry for the run around but as you probably have noted I am not allowed to post links here)
- which generates Computer Numerical Control (CNC) code which I've tested with CNC Simulator Pro but not on a real CNC cutter as yet.

Stop spamming.

You do not actually seek to discuss, you only seek traffic on your website.

_________________
The needs of the many outweigh the need of the few - Spock of Vulcan & Sentinel Prime of Cybertron ---proof that "the needs" are in the eye of the beholder.


Top
Display posts from previous:  Sort by  
Print view

Who is online
Users browsing this forum: No registered users and 0 guests
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
Jump to:   
cron

Delete all board cookies | The team | All times are UTC


This free forum is proudly hosted by ProphpBB | phpBB software | Report Abuse | Privacy