You're looking too deeply into this. I'm just trying to make Venn diagrams. Circles or squares or any arbitrary shape can represent the sets. The radii are arbitrary as are the location of the circles, the insides of which represent the contents of sets A, B, C, and E.
Venn diagrams are only intended to instill understanding in a problem. If the student understands them, great. If the student doesn't understand the concept, so what? It's not worth spending more than 30 seconds on.
We can do a two dimensional Venn diagram
Let set E of all triangles be arbitrarily illustrated by 0 to 100 on the number line.
Let set A of all isosceles triangles be represented by 50 to 75 on the number line.
Let set B of all equilateral triangles be represented by 70 to 75 on the number line.
Let set C of all obtuse triangles be represented by 30 to 55 on the number line.
Venn diagrams can be drawn one-dimensional or two-dimensional. The can also be represented by a three dimensional model. You could mathematically describe Venn diagrams in more than 3 dimensions.
Let me repeat, this is only to impart understanding. If someone doesn't understand, it is not worth spending more than 30 seconds on.
Regards,
Brian
----- Original Message -----From: Douglas AndersonSent: Sunday, October 28, 2007 8:50 AMSubject: Re: [Math4u] Please answer this question
I understand the circle formula for traingle E, but it isn't quite true as in the special cases when x or y = 0 you have a line rather than a triangle.Taking it further, your formula used is x^2 + y^2 = 100. Why did you choose 100, or is this just an arbitary value?
How did you decided by how much each circle was reduced in size, by how much each was shifted.E is a circlefine(or am I reading too much into this)But how can a circle represent the three special cases of traingles when clearly this is not the case. Take for example the obtuse or scalene triangle, the base would lie in the first quadrant, but the apex would be in the second quadrant.Or am I, as I asked earlier, looking to deeply when I shouldn't
On 10/28/07, Brian E. Jensen <brianejensen@prodigy.net > wrote:
http://www.mathopenref.com/isosceles.html
Isosceles triangle: A
triangle which has two of its sides equal in length.http://www.thefreedictionary.com/triangle
Isosceles triangle - a triangle with two equal sides
http://www.thefreedictionary.com/triangle
Equiangular triangle, equilateral triangle - a three-sided regular polygon
http://en.wikipedia.org/wiki/Isosceles_triangle
In an equilateral triangle, all sides are of equal length. An equilateral triangle is also an equiangular polygon , i.e. all its internal angles are equal—namely, 60°; it is a regular polygon[1] In an isosceles triangle, two sides are of equal length. An isosceles triangle also has two congruent angles (namely, the angles opposite the congruent sides). An equilateral triangle is an isosceles triangle, but not all isosceles triangles are equilateral triangles. [2]
E=set of all triangles. Represent this by the circle
X^2 + y^2 = 100
A=set of all isosceles triangles. Represent this by the circle
X^2 + (y-5)^2 = 25
B=set of all equilateral triangles. Represent this by the circle
X^2 + (y-7.5)^2 = 6.25
C=set of all obtuse triangles. Represent this by the circle
(x-5)^2 + y^2 = 25
Check:
A, B, and C are inside E.
B is inside A
A and C overlap
B and C must not overlap.
Distance between (0,7.5) and (5,0) is
Sqrt(5^2 + 7.5^2)
=sqrt((10/2)^2 + (15/2))
= sqrt(325/4)
Sum of radii = 2.5 + 5 = 7.5=15/2=sqrt(225/4)
sqrt(325/4) > sqrt(225/4) ok, the circles do not intersect.
Regards,
Brian
----- Original Message -----From: Rob van WijkSent: Saturday, October 27, 2007 2:34 PMSubject: Re: [Math4u] Please answer this question
Comments inside
-------- Original-Nachricht --------
> Datum: Fri, 26 Oct 2007 01:55:00 +0200
> Von: "Douglas Anderson" < djandersonza@gmail.com>
> An: Math4u@yahoogroups.com
> Betreff: Re: [Math4u] Please answer this question
> So what, would it be three circles (A,B,C) contained in a large circle E?
> I have to admit being an absolute tyro when it comes to Venn Diagrams as
> this request was the first time I have heard of them, yet the request
> piqued my interest.
> So as a tyro maybe I can help ch_mshahid with the help that Rob has
> offered.
> My error cam in because I misunderstood the wording. Actually, I read the
> query too quickly and thought he wanted one diagram to represent all
> possibilities.
> The three triangles, Isoceles can, in a special case, be considered
> equilateral. This would be the case when the base of teh triable is equal
> in length to the two sides. Hence every equilateral triangle is
> potentially isoceles.
> (Rob, would this be a correct assumption)
Actually, I have no idea what an isosceles triangle is (English is not my
native language); I'm perfectly sure I'd know if you told me the Dutch word
for it, but I'm very much pressed for time, so can't look it up, sorry.
> Now in the case of obtuse or scalene triangles. These to can be isoceles
> if two of the sides are of equal length. However, no scalene (obtuse)
> triangle could ever be equilateral.
> So as far as I can figure it, the cirlce representing equilateral
> triangles would be be wholly enclosed within the circle representing
> Isoceles triangles.
> Scalene can in special circumstances be Isoceles. Hence there would be an
> overlap between these two groups. However, since no equilateral triangle
> can be isoceles, there would be no overlap between these two, so
> (I have tried to include a sketch but cannot seem to have it included)
> B would be wholly indluded within A, and there would be an overlap
> between C and A but not C and B.
> Hope my words can portray what would have been better as a picture
Here's the picture (copy-paste to notepad or wordpad or whatever and choose
"Courier New" as font if it looks weird:
+--------------------+
| |
| +----------+ E |
| | | |
| | A +--+-----+ |
| | +---+ | | | |
| | | B | | | C | |
| | +---+ | | | |
| | +--+-----+ |
| | | |
| +----------+ |
| |
+--------------------+
(The original question also included a set E for Everything (all
triangles), which was missing from your post.)
HTH,
Rob
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Sunday, October 28, 2007
Re: [Math4u] Please answer this question
Thanks.
Hahahaha.
I know nothing about Vem diagrams and when the it looked interesting, so did a llittle research, very little.
But thanks for the info
On 10/28/07, Brian E. Jensen <brianejensen@prodigy.net> wrote:
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