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Question:i am doing a project and i was absent for the definition of skew lines. now we have to find examples of skew lines in real life.
for example and over pass on a highway?
please help me find image links or sites? Oh yeah and they have to demonstrate function
Answers:DEFINITION: Skew lines are lines that lie in different planes. They are neither parallel nor intersecting. http://go.hrw.com/resources/go_mt/hm1/so/c1ch8aso.pdf http://www.icoachmath.com/SiteMap/SkewLines.html Definition of Skew Lines: Two nonparallel lines in space that do not intersect are called skew lines. Reallife examples http://www.newton.dep.anl.gov/askasci/math99/math99236.htm Skewed lines are used a lot in construction. The best example that I can think of is the Brooklyn Bridge in New York. Here's a photo of it and you'll see all the lines that are not parallel. http://www.yellowecho.com/travel/brooklyn_bridge_16.html Also, it really depends on what angle you are look at something. We all know that the sides of a road/highway are parallel, but if you are driving on the road (the road in the photo of the Brooklyn Bridge is a perfect example), do you see how lines that we know are "parallel" can look skewed at the same time? The sides of the road are parallel, but our driving on the road and from the perspective of the driver, the sides of the road don't "look" parallel (even though looking down from the sky in an airplane they would look paralel), they look skewed from within a car. Same thing with railroad tracks... if you stand on the tracks and look down they look parallel, but if from where you are standing, and you look far into the distance... it looks like the two rail track converge to a point and aren't parallel. Same thing with like if you are looking down the school hallway. The walls are in reality parallel... but from where you are standing... and look straight ahead to the other end of the school building.. it looks skewed and like the lines are not parallel. Same with if you look at a building at an angle... we all know that in reality, all the ceilings and floors of your school are parallel (or I would hope that they are!!! LOL).... But if you look at the building from and angle... All the lines of your roof, floors and ceilings... all seem to converge to one single point... So reallife examples of parallel lines.... CAN and often do look like skewed lines if you are looking at an angle. Hope this helps...
Answers:DEFINITION: Skew lines are lines that lie in different planes. They are neither parallel nor intersecting. http://go.hrw.com/resources/go_mt/hm1/so/c1ch8aso.pdf http://www.icoachmath.com/SiteMap/SkewLines.html Definition of Skew Lines: Two nonparallel lines in space that do not intersect are called skew lines. Reallife examples http://www.newton.dep.anl.gov/askasci/math99/math99236.htm Skewed lines are used a lot in construction. The best example that I can think of is the Brooklyn Bridge in New York. Here's a photo of it and you'll see all the lines that are not parallel. http://www.yellowecho.com/travel/brooklyn_bridge_16.html Also, it really depends on what angle you are look at something. We all know that the sides of a road/highway are parallel, but if you are driving on the road (the road in the photo of the Brooklyn Bridge is a perfect example), do you see how lines that we know are "parallel" can look skewed at the same time? The sides of the road are parallel, but our driving on the road and from the perspective of the driver, the sides of the road don't "look" parallel (even though looking down from the sky in an airplane they would look paralel), they look skewed from within a car. Same thing with railroad tracks... if you stand on the tracks and look down they look parallel, but if from where you are standing, and you look far into the distance... it looks like the two rail track converge to a point and aren't parallel. Same thing with like if you are looking down the school hallway. The walls are in reality parallel... but from where you are standing... and look straight ahead to the other end of the school building.. it looks skewed and like the lines are not parallel. Same with if you look at a building at an angle... we all know that in reality, all the ceilings and floors of your school are parallel (or I would hope that they are!!! LOL).... But if you look at the building from and angle... All the lines of your roof, floors and ceilings... all seem to converge to one single point... So reallife examples of parallel lines.... CAN and often do look like skewed lines if you are looking at an angle. Hope this helps...
Question:As a followon to http://answers.yahoo.com/question/index?qid=20080404190545AAwI6UO
and referring to this diagram:
http://nrich.maths.org/askedNRICH/edited/2360.html
(but using my notation, not his)
I want to talk about the general eqn for line PQ, NOT just shortest distance itself.
Two questions:
1) Critique my working and suggest any improvements.
2) We end up with three eqns in two parametric variables (s,t).
How can we be sure that this overdetermined system has any solution in s,t?
Given any two skew (nonintersecting) lines:
Line LP : x = a + sb
Line LQ : x = c + td
>Hint: the line joining P and Q is perpendicular to both lines
PQ must be parallel to (a b), so form the unit vector in that direction:
n = (a b) / a b
Now take any (nonshortest) vector which is known to go between lines LP and LQ, such as (ca), and project it onto n:
a + sb (c a) . n n = c + td
(ac) (ac) . n n = (td sb)
=> Three eqns in two variables s,t I think the missing third variable is r, an arbitrarylength vector in the direction of n. => Three eqns in three variables
Or something like that. Please help tie up this loose end and rewrite:
(ac) (ac) . n n = (td sb) scythian  thanks.
It simplifies a bit if we write (ac) =u
in:
e = (ac) +Sb Td = u +Sb Td
Can you simplify your result algebraically? It looks like a determinant, or two separate determinants to me?
Answers:Let me try my hand in this. Let a, b, c, d be vectors in 3D space, and S, T be scalar variables, so that we have two skew lines a+Sb, c+Td. The difference, e = (a+Sb)  (c+Td), is a vector connecting the two lines, so that the shortest such vector would have the property e . b = e . d = 0. If we expand both, and solve the simultaneous equations, we end up with the following scalar quantities S, T: S = ((cd  ad) bd + (ab  cb) dd) / ((bd)  bb dd) T = ((ab  cb) bd + (cd  ad) bb) / ((bd)  bb dd) where ab, ad, cb, cd, bd, bb, dd are all vector dot products. Incidentally, the same result can be found by finding minimum S & T through partial differentiation of the vector length of e. Addendum: Well, let's see, if a  c = u, we can rewrite the equations as: S = (ub dd  ud bd) / ((bd)  bb dd) T = (ub bd  ud bb) / ((bd)  bb dd) The form does vaguely remind me of terms found in differential geometry, as for example EG  F , which is a determinant of the first fundamental form.
Answers:Let me try my hand in this. Let a, b, c, d be vectors in 3D space, and S, T be scalar variables, so that we have two skew lines a+Sb, c+Td. The difference, e = (a+Sb)  (c+Td), is a vector connecting the two lines, so that the shortest such vector would have the property e . b = e . d = 0. If we expand both, and solve the simultaneous equations, we end up with the following scalar quantities S, T: S = ((cd  ad) bd + (ab  cb) dd) / ((bd)  bb dd) T = ((ab  cb) bd + (cd  ad) bb) / ((bd)  bb dd) where ab, ad, cb, cd, bd, bb, dd are all vector dot products. Incidentally, the same result can be found by finding minimum S & T through partial differentiation of the vector length of e. Addendum: Well, let's see, if a  c = u, we can rewrite the equations as: S = (ub dd  ud bd) / ((bd)  bb dd) T = (ub bd  ud bb) / ((bd)  bb dd) The form does vaguely remind me of terms found in differential geometry, as for example EG  F , which is a determinant of the first fundamental form.
Question:more specifically around 15th century Europe and 12th19th century Japan.
Thanks You guys please read the fucking time period and region!
Answers:Gosh, you didn't even have a long question like most people do....lol. People have ADD reading just the first line.....those idiots...oh, I don't have an anwer either cause I don't remember the century you are asking about but atleast I read the question.
Answers:Gosh, you didn't even have a long question like most people do....lol. People have ADD reading just the first line.....those idiots...oh, I don't have an anwer either cause I don't remember the century you are asking about but atleast I read the question.
Question:I'm trying to build a model house for Geometry, and need some real life examples for these geometric shapes you may see in your house or on the outside of the house. Thanks!!!!
Transversal line
Parallel Lines
Kite
Alternate Interior Angles
SameSide Interior Angles
Corresponding Angles
Bonus Shapes Circle, Dodecagon
Answers:circle: Door knob parrallel line: on the windows... you could make it that certain type of window and include those three types of angles too...
Answers:circle: Door knob parrallel line: on the windows... you could make it that certain type of window and include those three types of angles too...
From Youtube
Just ASkew Music video :Mrs. Morales is a my geometry teacher.. i was assigned this duty to be her unveiling of the skew line dance... goes a little somethin like this I do not own any of the musc in this video and it belongs to the artist and companies alone. Have you ever had some work that you had to do, but when its all through, it was already due! Let me tell y'all a story 'bout my situation, I was caught up in some troubles cause procrastination! I didn't know what a skew line was! When I found out theres a dance I just thought faux pas! You put your hands wherever you select, just make sure they dont intersect! Oh baby you! you got what I need! Oh in geometry oh oh in geometry! You you got what i need....... I'm so corny!! haha enjoy :)