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A rectangle is a parallelogram.
A rhombus is a parallelogram.
A square is a rectangle.
A square is a rhombus.
In which geometries are all these still true, and why?
Euclidean (obviously)
non-Euclidean
Riemannian
etc.
I'm thinking that some shapes may not exist in some geometries. Do any exist that still negate the statements made?
P.S. - Geometry was my least favorite math.
There are II kinds of people in the world, those who understand binary and those who understand Roman numerals. Web - Blog - RSS - Math
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If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
[my articles]
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No, Math++.
There are II kinds of people in the world, those who understand binary and those who understand Roman numerals. Web - Blog - RSS - Math
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I try to guess that multiple inheritance applies also to non-Euclidean geometries if you generically define the rectangle having all angles equal and rhombus having all sides equal and, finally the square having both properties (i.e. you don't insist on 90 degrees angles).
Probably I'm wrong since I'm really know nothing about non-Euclidean geaometry  .
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
[my articles]
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I don't think you can re-define the rectangle and the rhombus, it would be cheating...
The only difference between the Euclidian and non-Euclidian geometries is the 5th postulate, but the other ones stand. So you must have a definition of "right angle" in every geometry, which means you can define the rectangle in every geometry.
Admittedly, the definition may become very obscure and complicated... and you probably would not be able to measure the right angle in degrees or radiants...
So I think the multiple inheritance holds in every geometry.
The square is defined to be something that is both a rectangle and a rhombus, and because you can define the rectangle and rhombus in every geometry, you can define the square in every geometry.
[edit] I realised this may not be very clear... my point is that when you change geometry, the only thing you re-define is the basic concepts like line, lenght, and right angle, but the rectangle, rhombus and square have the same definitions, just expressed in the new interpretation of line, lenght, and angle.
-+ HHexo +-
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Nope, I'm not cheating, a rectangle may really be defined, in Euclidean geometry as a quadrilateral having all of the angles equal, the fact that then they are right angles is then a mere consequence  .
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
[my articles]
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CPallini wrote: mere consequence
Visually it is mere, but trying to prove that may get you stuck on the 5th Postulate, which made me wonder if my original statements always hold true.
There are II kinds of people in the world, those who understand binary and those who understand Roman numerals. Web - Blog - RSS - Math
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IMHO the point is not if you need or don't need the fifth postulate.
If you define a rectangle as the quadrialteral having all its angles equal then yes, you may need the fifth postualte to demonstrate that the angle are in fact right ones, but it doesn't matter: in the context of Euclidean Geometry the fifth postulate is fine (correct me if I'm wrong, since I'm not an expert about), but with the above definition (the all agles equals one), the proposed inheritance tree is valid also in not-Euclidean geometries (Maybe I'm wrong again).
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
[my articles]
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But a rhombus is a diamond... leading to diamond-shaped Multiple Inheritance which is naughty. 
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I am trying to find an algorithm, or actual code if available, to find the intersection point of a Great Circle line and a straight line. Even though this is on a sphere, the earth, I want to consider the straight line as basically tunneling through the earth and not following the curvature of the earth. Basically I want to find the point where a Great Circle line passes some "line in the sand". I have searched for an algorithm for this but have not been able to find anything. Please help me Obi Wan Kenobe, you're my only hope.
Kalvin
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Hi,
there is no algorithm involved, just a little algebra, with a system of two equations (line and
sphere) to solve. What do you know about the line? What is your coordinate system?
If you can't solve it in three dimensions, try the similar question in two dimensions first.
Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips:
- before you ask a question here, search CodeProject, then Google;
- the quality and detail of your question reflects on the effectiveness of the help you are likely to get;
- use PRE tags to preserve formatting when showing multi-line code snippets.
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Thank you for the reply.
When it comes to math I am at a disadvantage. My lines are defined by lat/lon values for the end points of both lines. I know the equation for a straight line is y=mx+b. I can plug in lat/lon for y and x since lat/lon are in decimal degrees. I have not been able to find an equation for the Great Circle line, not one I understand anyway.
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Why don't you follow Luc suggestion and try first in two dimensions?
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
[my articles]
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That's a great idea. Since the great circle is on a sphere, could I use an arc in 2D for this? Any idea what the equation of a Great Circle line is?
I really appreciate the help. I have been looking at this for days and am getting nowhere. All the equations I find have to do with finding the distance or heading for a Great Circle line. I don't need either one of those.
Kalvin
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Well, I think that we have too few details of your problem. For instance do you mean a 3D generic line? Moreover, what Great Circle? Have you considered that a sphere has infinite (with power two, if I'm not wrong) Great Circles?
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
[my articles]
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I couldn't pass this by without a comment. Two points on a sphere (except the endpoints of a diameter) can have one and only one great circle pass through them. The two points and the center of the sphere define a plane, and this plane intersects the sphere in one great circle.
What you are referring to, I think, is that two points in space can have an infinite number of circles pass through them, bounded, of course. The smallest circle is the one whose diameter is the line defined by the two points. The infinity starts there, a different circle for every increase in size, and these circles are just tangent to the two points. The additional infinities are the rotation of any of the circles around the line thus forming a torus. The interesting point is that these two sets of infinities are a distinct set of circles than those created by changing the end points of the same line, (a lower bound for the smallest circle and all such circles are distinct from the initial set, even if the same diameter, because the center is at a different place). Same thing for a different line (two different points not on the same line).
As to the initial question, I do have the equations to solve this, but this bring up analytical geometry and vector methods. I could elaborate if anyone is interested.
Dave Augustine
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Member 4194593 wrote: I couldn't pass this by without a comment. Two points on a sphere (except the endpoints of a diameter) can have one and only one great circle pass through them. The two points and the center of the sphere define a plane, and this plane intersects the sphere in one great circle.
Sphere has infinite power two Great Circles, if you fix two points, it is strighforward that you end up with no degrees of freedom, i.e. one Great Circle.
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
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If you read the authors second post, it was stated that both lines were defined by lat/lon values, thus only one great circle.
Dave Augustine.
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Member 4194593 wrote: both lines
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
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Hi every body.
Can any body help me plz
I have a task that requires to read the text on a image
My requirement is
I take a image of a vehicle number plate through a web cam or a usb camera.
Now when i get the image when i click a button i should get the numberplate number into a text box I need this functionality using c#,vb.net plz help me i am doing my B.tech final year project, I would be very much thank full if any one will help me
thanks in advance
with regards
harivinod
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You posted your question in 4 different forums huh? How rude. Read the forum rules. All this time you spent cross-posting, and waiting for someone to reply, you could have done research to get the answeres yourself.
I'm going to become rich when I create a device that allows me to punch people in the face over the internet.
"If an Indian asked a programming question in the forest, would it still be urgent?" - John Simmons / outlaw programmer
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Awww, geeze. OP posted here, too 
"I guess it's what separates the professionals from the drag and drop, girly wirly, namby pamby, wishy washy, can't code for crap types." - Pete O'Hanlon
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I am attempting to come up with an algorythm for ranking players in a multiplayer game. The ELO system (used in Chess et-al) does not seem to fit as that is geared towards head-to-head games and im dealing with a variable player-number multiplayer game.
I basically have 4 (possibly 5) "statistics" that I can capture about a players history. I may want to weight some of those statistics more than others.
Can anyone start me off on how to proceed?
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What about MS TrueSkill?
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
[my articles]
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