Lines a and b are parallel. D is a point not on a or b. Using only a straightedge, construct the line through D parallel to a and b.
>>7968193
this is impossibly easy. Just set up your straight edge so that it doesn't intersect line a.
>>7968203
Duh? Parallel?
>>7968193
draw a line through point D. Put 2 tick marks on each line a,b and your new line. This signifies they are parallel
>>7968240
>Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.
>>7968267
You absolute complete fucking div. Of course I know what parallel means. Poster 2 obviously doesn't or was having an Alzheimers attack.
>Just set up your straight edge so that it doesn't intersect line a.
Lot of room for that to not be parallel.
>>7968296
how? if it's an ideal straight edge it would have infinite length and it would produce a straight line. A straight line that doesn't intersect another straight line in the same plane are parallel. There's no room for it not to be.
>>7968296
He obviously assumed a (and b) continue like that infinitely in both directions, and the straight edge does as well
>>7968300
I think the challenge is to work it out geometrically rather than have an infinite straightedge Kobayashi Maru.
>>7968314
the whole point of a straightedge is that it's infinite in length. There is no "unit" otherwise you should refer to it as a ruler.
>>7968300
>an ideal straight edge it would have infinite length
https://www.google.com/search?q=pedant
>>7968203
OP here
I think this could be seen as a type of neusis. The Ancient Greeks would wreck your shit if they found out.
>>7968339
>...this could not be done in a finite amount of time
We can't add infinite sums in finite time either, did the question give me a fucking time limit? Wildberger gtfo.
>>7968339
>Even if such a thing existed...
I don't think you understand that math isn't interested in objects that actually exist. For example, a line with no width.
Is this even possible without a compass?
>>7968495
I've been trying various intersections but no good. Think it probably would need a compass.
There's no reason you'd theoretically need a compass to make a lane perpendicular to a and b. Just line end of the straightedge up with a or b and make a perpendicular line through d, then at d make another perpendicular line doing the same method. repeat on the other side. done. there will always be an inaccuracy even with a compass but this method is still fairly accurate.
>>7968495
Yes it is. I have a solution in 7 lines, including the desired line.
It's a bit unfair, though, since the theorem that justifies the construction is rather obscure.
>struggling with basic classical construction concepts
Here we go:
1. With compass on D, use any big enough radius to draw an ark that intersects a, creating E over a.
2. With compass on E and the same radius as before, draw another ark that intersects a at F.
3. With compass on F, draw one last ark that intersects the ark built in step 1 at G.
4. With straightedge, draw a line connecting D and G.
There are probably easier ways to do it, but I can't remember any other simple method off the top of my head. I'm too lazy to draw what I just described, but you'll basically build a parallelogram using point D as one of the vertices and line a as one of the sides. The steps were not very detailed and lack some necessary information that are easily deduced, but if you have any questions about it, feel free to ask. Also, if someone would be willing to test it out for fun on any program to see if it actually holds up, that would be nice.
Choose two different points A and B on a.
Lines AD and BD intersect line b at C and E.
Lines AE and BC intersect at F.
Lines FD and AB intersect at G.
Lines CG and BD intersect at H.
Lines AH and BC intersect at I.
Then line DI is parallel to the given lines.
This works unless D happens to have equal distances to both parallel lines. In that case just choose another point in the plane, draw a parallel to the given lines through this point using the previous construction, and finish by applying the construction with this line and one of the original lines.
>>7968193
If you can't construct such a line then a and b are not parallel. Give all 3 lines the same slope and they will not intersect.
>>7968618
You can't make perpendicular intersections with a straight edge. This is a formalized geometrical problem, not an eyeballing one.
>>7968663
>struggling with basic reading comprehension
>>7968355
>I don't think you understand that math isn't interested in objects that actually exist. For example, a line with no width.
I understand that fine.
I also understand a straightedge ISN'T one of Plato's "ideal forms".
It's a physical object often used in geometry.
>did the question give me a fucking time limit?
No, but you claimed it could be done with your method, and yet it clearly can't, since you will never finish the task given your solution.
>>7968745
Mathematical problems involving straight edge and compass ARE idealized and not about physical straight edges. However you are correct that his answer would not be accepted because historically these problems allow arbitrary numbers of steps but not infinite.
>>7968664
Choose points E and F not collinear to D and not on a or b.
Lines DF and b meet at G.
Lines DE and a meet at H.
Lines FH and b meet at I.
Lines EG and a meet at J.
Lines EI and FG meet at K.
Then DK is parallel to a and b.
This doesn't work if E or F happen to lie on the desired line.
>>7969064
>Lines EI and FG meet at K.
That should be FJ
>>7969064
Ah yes, that's a better way to do it.
>>7969064
looks like a triangular resection with two redundancies
>>7968193
Everyone in this thread is a moron
HINT: draw lines AD BD and AB
If you can't see it within 10 seconds, kill lyourself
>>7968193
wouldnt you just get a straight edge that was the width of the gap between either a-d or b-d
and mark a line?
>>7968664
Crap, in trying intersections I didn't think outside the lines.
