Projective Geometry
Páginas: 3 (526 palabras)
Publicado: 21 de octubre de 2012
PROJECTIVE GEOMETRY
INTROCUCTION: Why I chose this topic?
I chose this topic because I think it is interesting and easy to understand because this is one of the few mathematical topics which canbe seen in real live.
DEVELOPMENT:
OUR KNOWLEDGE:
We know in Euclidean geometry that all two lines on a plane can be parallel lines or this two lines intersect at a point and the same happentotwo parallel lines or any 2 planes at the space.
HISTORY:
Renaissance artists observed that to make a realistic drawing had to draw it as if you were to look with one eye only (one outbreak) andprojected it so from any point from which we look at our brain make it look three-dimensional. Thus Renaissance artists developed drawing techniques called "methods of perspective"
INITIATION:What I don't understand is why they made it from wide to narrow.
In the seventeenth century Gérard Desarges actually observed when looking to infinity our optical perspective makes it appear thateverything comes together at the same point so that he thought could be true, he showed that all lines in the plane intersect at a point at infinity (space) ("two distinct lines determine a uniquepoint" which called point at infinity using the techniques "methods of perspective", Desargues developed an alternative way of constructing perspective drawings by generalizing the use of vanishing pointsto include the case when these are infinitely far away.
From that time mathematicians like Euclid, Poncelet, Hilbert discovered many results and made the projective geometry which is much simplerthan the Euclidean geometry so helped solve many problems which had not been able to solve the Euclidean geometry, although later was shown to be extrapolated (convert) all the results of a geometry toanother.
The project was completed in the 20th century when Einstein proved that the universe can be better interpreted with projective geometry (Astronomy)
EXAMPLES:
One of them is when...
INTROCUCTION: Why I chose this topic?
I chose this topic because I think it is interesting and easy to understand because this is one of the few mathematical topics which canbe seen in real live.
DEVELOPMENT:
OUR KNOWLEDGE:
We know in Euclidean geometry that all two lines on a plane can be parallel lines or this two lines intersect at a point and the same happentotwo parallel lines or any 2 planes at the space.
HISTORY:
Renaissance artists observed that to make a realistic drawing had to draw it as if you were to look with one eye only (one outbreak) andprojected it so from any point from which we look at our brain make it look three-dimensional. Thus Renaissance artists developed drawing techniques called "methods of perspective"
INITIATION:What I don't understand is why they made it from wide to narrow.
In the seventeenth century Gérard Desarges actually observed when looking to infinity our optical perspective makes it appear thateverything comes together at the same point so that he thought could be true, he showed that all lines in the plane intersect at a point at infinity (space) ("two distinct lines determine a uniquepoint" which called point at infinity using the techniques "methods of perspective", Desargues developed an alternative way of constructing perspective drawings by generalizing the use of vanishing pointsto include the case when these are infinitely far away.
From that time mathematicians like Euclid, Poncelet, Hilbert discovered many results and made the projective geometry which is much simplerthan the Euclidean geometry so helped solve many problems which had not been able to solve the Euclidean geometry, although later was shown to be extrapolated (convert) all the results of a geometry toanother.
The project was completed in the 20th century when Einstein proved that the universe can be better interpreted with projective geometry (Astronomy)
EXAMPLES:
One of them is when...
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