a scalene and isosceles triangle are also "regular" - don't tell me they aren't cause last yr in maths comp, a scalene was considered "regular" and i put it down as irregular and i got it wrong.

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- May 27th 2006, 11:53 PMconfused
a scalene and isosceles triangle are also "regular" - don't tell me they aren't cause last yr in maths comp, a scalene was considered "regular" and i put it down as irregular and i got it wrong.

- May 28th 2006, 12:00 AMCaptainBlackQuote:

Originally Posted by**confused**

see MathWorld.

Also, your pentagon is not regular.

RonL - May 28th 2006, 12:03 AMconfused
then i can only conclude that the board of studies are bull****

- May 28th 2006, 12:04 AMCaptainBlackQuote:

Originally Posted by**confused**

RonL - May 28th 2006, 12:05 AMconfused
i can't even think why skool is "compulsory".....so sad

- May 28th 2006, 10:25 AMSoroban
Hello, Chuck_3000!

Quote:

Certain sets of regular polygons fill space around a point without gaps or overlapping.

e.g. imagine 3 hexagons joined together and the common vertice is the point they surround.

That is classified a [6,6,6] point fill set (3 six sided shapes)

Although the polygons can be arranged in a different order, we count these as the same.

We call a set of regular polygons filling space around a point a**point-fill set**.

a) Find a point-fill set of 3 polygons containing a 24-gon

b) Explain why it is not possible to have a point fill set containing a triangle and a pentagon

c) Find all point-fill sets that contain at least one square.

The interior angle of a regular -gon is: .

Armed with this formula, you can make a list:

(a) A 24-gon takes up of the circle about the point,

. . leaving to be filled.

This can be accomplished with a triangle and an octagon .

(c) Of course, four squares comprise a point-fill set.

With two squares, there are to be filled.

This can be accomplished with:

. . three triangles:

. . a hexagon and a triangle:

With one square, there are to be filled.

This can be accomplished with:

. . two triangles and a 12-gon:

. . a hexagon and a 12-gon:

. . two octagons:

. . a pentagon and a 20-gon:

I hope I didn't miss any . . .

- May 30th 2006, 10:09 AMMathGuru
The question asked in an Australian take-home competition. In case you wanted just to check, it is the:

2006 Maths Challenge Stage

Mathematics Challenge for Young Australians

TERM 2

JUNIOR STUDENT PROBLEMS

An Activity of the Australian Mathematical Olympiad Committee

A Subcommittee of the Australian Mathematics Trust in association with the Australian Academy of Science and the University of Canberra

...Just google Australian Mathematics Trust Maths Challenge or something like that ;)

This person happened to be trying to complete one of the hardest questions in the book - well, it's hard until you figure out the key point to it, then it's easy. I'm just not satisfied this thread is still up there, and she/he's been given the answers. Unfortunately/Fortunately, I don't think she/he'll be able to write a 1 to 2 page explanation on Egyptian algebra and other techniques =) Especially not since they're probably about 13. There's another easier way...

This competition is due on Wednesday ((GMT+10:00 Sydney))...so it won't make much of a difference if it isn't deleted or not, just as long as no-one else posts answers anymore.