[seqfan] Re: Number of Equilateral Triangles in Regular 3n-gon

[Antreas Hatzipolakis]

A related problem:

How many triangles can be formed from the vertices of a regular polygon
with 13 sides so that the inside of each of the triangles contains the
center of the circle circumscribing the polygon?

Reference:
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=46&t=558360&

Generalization for regullar 2n+1-gon.

Antreas


On Tue, Apr 9, 2013 at 1:04 AM, Antreas Hatzipolakis
<anopolis72 at gmail.com>wrote:

> Yes, the same problem.
>
> We can also ask the same question for the complete regular 3n-gon
> (by taking the extensions of sides and diagonals)
>
> APH
>
>
> On Tue, Apr 9, 2013 at 12:39 AM, Giovanni Resta <g.resta at iit.cnr.it>wrote:
>
>> On 04/08/2013 09:07 AM, Antreas Hatzipolakis wrote:
>>
>>> Which is the number of the regular triangles bounded by sides and
>>> diagonals
>>> in a regular 3n-gon?
>>>
>>
>> I got
>> 1, 14, 69, 188, 465
>> as the first 5 terms, but I'm not completely sure
>> about these values.
>>
>> I have created a picture of the 69 triangles in the 9-gon,
>> grouped by size, here : http://www.iread.it/triang.png
>> just to check we are talking about the same problem.
>>
>> Giovanni
>>
>