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Topic: Classification of quadrilaterals
Replies: 17   Last Post: Jan 11, 1995 6:43 AM

 Messages: [ Previous | Next ]
 William T. Webber Posts: 16 Registered: 12/3/04
Re: Classification of quadrilaterals
Posted: Dec 21, 1994 8:26 AM

On 21 Dec 1994, Chenteh Kenneth Fan wrote:

>
> But I at least offer these:
>
> 1. Which quadrilaterals tesselate the plane?
>
> 2. (i'm groping) Given a tesselation of the plane into congruent triangles,
> which quadrilaterals can be formed from a finite union of these triangles?
>
> 3. (groping...groping...) Which quadrilaterally shaped billiard tables
> allow for ball trajectories which touch fewer than four sides? (no friction...
> no ball size...cross reference this weeks problem of the week!)
>
> (Note: the answers to these all include the trapezoids...but the answers
> do not include generic quadrilaterals.)
>
> Ken

I haven't looked into the second and third, but it is not true that general
quadrilaterals do not tile the plane. -To make that a positive statement-
Any quadrilateral will tesselate the plane. There is no restriction on the
quadrilateral (not even convexity).

Will Webber

Date Subject Author
12/15/94 E7M2WAT@TOE.TOWSON.EDU
12/16/94 W Gary Martin
12/16/94 Henri Picciotto
12/17/94 John Conway
12/17/94 roitman@oberon.math.ukans.edu
12/18/94 John Conway
12/20/94 Chenteh Kenneth Fan
12/21/94 John Conway
12/21/94 Walter Whiteley
12/21/94 William T. Webber
12/21/94 James King
12/21/94 Chenteh Kenneth Fan
12/21/94 John Conway
12/21/94 John Conway
12/21/94 John Conway
12/21/94 Chenteh Kenneth Fan
12/21/94 Chenteh Kenneth Fan
1/11/95 joe malkevitch