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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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.
It is not only me telling you that a regular 3-gon is an equilateral triangle,Quote:
Originally Posted by confused
see MathWorld.
Also, your pentagon is not regular.
RonL
then i can only conclude that the board of studies are bull****
It is not unknown.Quote:
Originally Posted by confused
RonL
i can't even think why skool is "compulsory".....so sad
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 upof the circle about the point,
. . leavingto be filled.
This can be accomplished with a triangleand an octagon
.
(c) Of course, four squares comprise a point-fill set.
With two squares, there areto be filled.
This can be accomplished with:
. . three triangles:
. . a hexagon and a triangle:
With one square, there areto 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 . . .
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.