lbiarge

1 - first TED video is more easy to see here (add h por http): 2 - Curious like a person can say many words and say nothing. (in the video). 3 - I believe I understand geodescis and also like gravity curve the geodesic where travel the photons, ... According to geodesic you consider that a point 3d xyz after a conversion o geodesical change from Euclidian to hyperbolic, ... the point xyz remain at same point 3d because you represent that point in a 3d coordenates without consider that hte geometry has changed. An example: 10 is a mathematical value, but according by the base can to means 2 (binary), 10 (decimal), 16 (hexadecimal), ... but according you say only count that it's 10, by that you consider that 10 binary = ... = 10 hexadecimal and by that that 2 = .... = 16 Another example, light in universe travel by the geodesic, so near a mass the "straght line" without consider the mass is curved, really is straight but according to your geometry it would be curved and by that in a point would to be many parallels but really if you consider the so curved line light a "straght line" that change the geometry from euclidian to hyperbolic or another really only can to be 1 parallel in that point. So wiithout consider that the geodesic is curved by gravity seem that the light is curved but knowing that mass curve the geodesic understand that really travel a "straght line". 4 - The TED video show a piece with more that one parallel that supposed parallels cannot to be parallels between theirs (1 common point) or only 1 parallel at any time and changing the geometry and by that the point xyz change. Really the geometry in parallels and triangle is like a sheet of paper, draw a triangle or a parallel, know you can roll the paper in hyperbolic form and the parallel is only one, the point xyz change and the triangle adopt the adecuate form. Please draw me more that 1 parallel in 1 point (withot the TED absurd form) or draw me a triangle with 2 angles of 90º, not affirm, draw me, When I speak over cones I really speak over perimeter of cone without the base, this has 2 angles of 90º, and 1 more angle but the line that joint the 2 angles of 90º is equidistant to the other angle and by that is not straight and by that is not a triangle. The example of the meridians in same form not is usefull because the line from equator is equidistant to the pole. Thanks. Another example: According to relativity theory a man that travel in a rocket a hight speed the time go slowly (person 1). So according to this in time x the rocket and another person in Earth (personn 2) consider time x, 1 year later in Earth (consider time present) occurs 2 things. 1 - present time is for person 1 and 2 2 - if we consider time x + 1 year the time is different by the 2 persons. In same form a triangle or parallel in Euclidian geometry can to be represented in hyperbolic, ... but the position xyz change, not remains same in same form that in 2 the x + 1 year is not the same for both persons of the example or that 10 is not the same in binary that in decimal. In the example of corals, ... the 2 sides of the coral or the worms only are paralels in a geometry according to that and the point is the same that in a flat Euclidian geometry when are parallels and the xyz point change and by that are not multiples parallels in a point because the point xyz always is the same, only change the geometry according to the movement of the worm.

AC and AB are meridians not parallels the line from A to B is equidistant to C, this is a semi-sphere not a triangle. A cone and a semi-cone also have 2 angles of 90º but the line of equator is equidistant to the pole. A cone and a semi-sphere are not triangles. Also 3 angles unit by not straight lines can to sum from 0º to 360x3º A triangle need to be 3 straight lines, not only 3 lines. In that hyperbolic geometry:that show like triangle are 3 angles unit by not straight lines. A triangle is formed by 3 angles and straight lines union, if you take that supposse triangle and put in a plane you can see they have not straight lines. Draw me a triangle with 2 angles of 90º. Please. Thanks. Do you speak of maths of doy you speak over fiction? Do you know any train that travel by 2 ways that join in any point of the world? Do you really believe that 2 parallels join in any point of the universe? Do you know any triangle with 2 or 4 angles? Please speak over maths not over fiction. Thanks. To say that "So intuitively, a given pair of parallel lines would intersect at a "point at infinity"" is near same that to say that x and x+1 in near infinite has a different distance less or more that 1 and by that that maths is not science.

In classical maths from Euclid believed that a triangle is 180º and that in 1 point only can travel a parallel to other. – http://en.wikipedia.org/wiki/Parallel_postulate So determine that “At most one line can be drawn through any point not on a given line parallel to the given line in a plane” Lately Non-Euclidean geometry says that “Either there will exist more than one line through the point parallel to the given line or there will exist no lines through the point parallel to the given line” – http://en.wikipedia.org/wiki/Non-Euclidean_geometry#History According to this new geometry (has more that a century), by a point can exist more that one line, so according to parallel definition this more that 1 line would be parallels to the first line but not parallels between theirs (they have 1 common point). In same form would occurs the same in the infinites points that use these multiple parallels, all that billions of lines would be parallel to the first line and not parallels between theirs. By reciprocity in all or many of the points of the first line would exist many parallel lines parallel to any point of the millions parallels lines to the first, but not parallels between theirs. According to this we cannot say that a parallel from a parallel are also both parallels. By that probably the geometry would need to go out of the maths. xxxxxxxxxxx But there are more: According to hyperbolic geometry (the acute case) and elliptic geometry (the obtuse case) the sum of angles of a triangle can to be more or less of 180º : “The sum of the measures of the angles of any triangle is less than 180° if the geometry is hyperbolic, equal to 180° if the geometry is Euclidean, and greater than 180° if the geometry is elliptic” according to http://en.wikipedia.org/wiki/Non-Euclidean_geometry#History By that they give an example of a triangle formed by the equator of the Earth and meridians that with 2 angles of 90º have another angle in the pole and so add more of 180º. According to this: 1 – Know parallel lines can not be parallels, because according to this 2 lines with 90º angle (parallels) make a triangle. So to the before note of that in a point can to be more or a parallel also can affirm that a parallel also can not to be a parallel. 2 – A semi-sphere is not a triangle, in the example the line of the equator is equidistant to the pole angle and by that is a line but is not straight. Really in semi-spheres, cones and semi-cones there is near a triangle (it has 2 angles of 90º and 1 more), but semi-spheres and semi-cones are not triangles and the line between the 2 angles of 90º is equidistant to the other angle. If I could make a triangle with lines not straight I could make triangles from 0º to 360×3º (less the minimum angle we consider x 3), but a triangle has 3 straight lines and 3 angles. Really in hyperbolic and elliptic geometries the triangles really are also of 180º. How? easy: make a triangle in a sheet of paper and now you can curve the paper in hyperbolic to see the result of a hyperbolic triangle, … also you can bend the paper in the form you like to understand how would be a triangle in any other geometry environment. Also for parallels in a hyperbolic geometry would seem a parallel different from a elliptic geometry but an space cannot to be at same time hyperbolic and elliptic and like in the case of triangle the result is to make 1 or more parallel in a sheet of paper and bend the paper if you bend the paper the position of the parallel and point change thinking in a 3d space because the space has changed. By that really is 1 only point or parallel but like in the case of sheet of paper bended the parallel and point has changed their position. You cannot thing in a 3d space in that change the parallel because if you change the geometry also the point changes of position. Proof with the sheet of paper to see that positions of the points are different but by the same point only is 1 parallel. To say that are many parallels in a point would be like to say that New York is in infinite possitions because the Earth turn and has translatation without consider that time is a dimension. Also in sphere and cones,… you can use the triangle of the sheet of paper to see the form of a triangle in this form. If this they say a train that travels by parallel railroad could not travel because the railroad would change the separation. Remember that a triangle can to be made in 2d and at least in 3d because in 3d 3 points make a plane. I don’t understand very well how mathematicians have admitted this impossible near of 100 years because is worse that a bad novel fiction. The classical scientists create in Earth parallels and meridians for localization in Earth because the meridians are not parallels, they understood well the maths principles but actual scientists have mistake all this information. If this Non-Euclidean geometry would true: 1 – would not exist the parallels because many parallels in 1 point is same that not exist parallels because have 1 common point, also the triangle with parallel lines that have a common angle. 2 – Geometry would to go out of maths because to say that a triangle can to have more and less of 180º is so math that to say that 2+2 can to be 4 and more and less of 4. 3 – Trains could not work because would not exist parallel lines. xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx With same example of parallels we would say that 10 is many result like 1+1=10, 1+2=10,1+3=10, … 5+5=10, 8+8=10 because 1+1 is 10 in binary, 5+5=10 in decimal and 8+8=10 in hexadecimal and also with same example of triangles we would with 3 point in 3d you can draw infinites triangles because can to be in hyperbolic, elliptic and euclidean geometry without have importance that the points change of position like in the example of the sheet of paper when you bend it and by all this kill the maths because are not exact (in this examples arithmetic and geometry). xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx You can proof what I say is false (remember that who affirm anything is who need to give the burden of proof): 1- Proof with real example that in a point you can put more of 1 parallel to a line. 2- Draw a triangle with 2 angles of 90º. xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx Luis Biarge Baldellou This note is posted in public domain and copy in this page: http://imagineonscience.wordpress.com/triangles-and-parallels/ Thanks.