Page 2 of 2 FirstFirst 12
Results 16 to 22 of 22

Math Help - Polygons at a Point

  1. #16
    Newbie
    Joined
    May 2006
    From
    ontario
    Posts
    7
    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.
    Follow Math Help Forum on Facebook and Google+

  2. #17
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by confused
    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,
    see MathWorld.

    Also, your pentagon is not regular.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Newbie
    Joined
    May 2006
    From
    ontario
    Posts
    7
    then i can only conclude that the board of studies are bull****
    Follow Math Help Forum on Facebook and Google+

  4. #19
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by confused
    then i can only conclude that the board of studies are bull****
    It is not unknown.

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #20
    Newbie
    Joined
    May 2006
    From
    ontario
    Posts
    7
    i can't even think why skool is "compulsory".....so sad
    Follow Math Help Forum on Facebook and Google+

  6. #21
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,683
    Thanks
    615
    Hello, Chuck_3000!

    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 n-gon is: . \frac{n-2}{n}\cdot180^o

    Armed with this formula, you can make a list:

    \text{Triangle: }60^o\quad\text{Square: }90^o\quad\text{Pentagon: }108^o\quad\text{Hexagon: }120^o

    \text{Octagon: }135^o\quad\text{Decagon: }144^o\quad\text{12-gon: }150^o\quad \text{15-gon: }156^o

    \text{18-gon: }160^o\quad\text{20-gon: }162^o\quad\text{24-gon: }165^o

    \text{30-gon: }168^o\quad\text{36-gon: }170^o


    (a) A 24-gon takes up 165^o of the circle about the point,
    . . leaving 360^o - 165^o \:=\:195^o to be filled.
    This can be accomplished with a triangle (60^o) and an octagon (135^o).


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

    With two squares, there are 180^o to be filled.
    This can be accomplished with:
    . . three triangles: 3 \times 60^o
    . . a hexagon and a triangle: 120^o + 60^o

    With one square, there are 270^o to be filled.
    This can be accomplished with:
    . . two triangles and a 12-gon: 60^o + 60^o + 150^o
    . . a hexagon and a 12-gon: 120^o + 150^o
    . . two octagons: 135^o + 135^o
    . . a pentagon and a 20-gon: 108^o + 162^o


    I hope I didn't miss any . . .
    Follow Math Help Forum on Facebook and Google+

  7. #22
    Site Founder MathGuru's Avatar
    Joined
    Mar 2005
    From
    San Diego
    Posts
    478
    Awards
    1
    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.
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. similarity of two polygons
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 10th 2010, 04:59 AM
  2. Polygons
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 26th 2007, 09:27 AM
  3. polygons and triangles
    Posted in the Geometry Forum
    Replies: 9
    Last Post: July 5th 2007, 11:27 AM
  4. Polygons
    Posted in the Statistics Forum
    Replies: 3
    Last Post: January 25th 2007, 03:25 PM
  5. Polygons Help!
    Posted in the Geometry Forum
    Replies: 4
    Last Post: January 6th 2007, 06:06 AM

Search Tags


/mathhelpforum @mathhelpforum