Lines

A professor in the math department is teaching geometry. The topic for the day was called "Shapes".



The professor start the class by drawing some figures on the board: lines, circles, rectangles and triangles.



On the right side of the board, he draws two lines.



"Hello bro", says the line 1 to the just created line 2, "long time no see".



"Yeah", says line 2 "The last time the old geezer drew us, we were part of the complex cartesian equation and he made us meet at an absurd point on the blackboard!"



"I hope he doesn't do that again", says line 1 agreeing.



The professor turns around to the class and explains,



"Parallel lines", he states "in Euclidian geometry, are lines are that never intersect when they are drawing in the same plane. In other words, all points on the lines are equidistant from each other at all times".



"As you can see, I just drew a pair of parallel lines. It is their destiny never to meet; no matter how far you extend them!"



"What the..." says line 1



"How dare he? We are brothers, we always meet when we are created, no matter what!" says line 2 angrily.



"True, it is matter of honor! We will prove the old professor wrong"



The two lines start moving across the blackboard determined to change their destinies.



"Why do you fight your fate so hard?", says a voice behind them. It was a circle.



"Everything that goes around comes around" says the circle in a cynical tone. "It is the wheel of fate, no matter how fast you turn it you return to the same point".



"But we are brothers, shouldn't brothers always meet up?" asks line 1



"You see, every point on me is equidistant from the center much like the two of you are equidistant from each other. It's a vicious loop!", says the circle seriously.

"Don't listen to the circuitous old rogue. He has a roundabout way of convincing you", shouts line 2.



"Yeah, let's move on!", says line 1 and the two of them carry on with their journey.



"You cannot deny your rectilinear properties", interrupted a voice after a while. It was a rectangle facing them now.



"What do you mean?" asks line 1



"It's all got to do with angles you know...Two of my arms are perpendicular to each other., while the other two never meet", says the rectangle in rigid voice.



"Oh" exclaimed both the lines, comprehension dawning on them.



"You mean to say?"



"Yes, there is no angle between the two of you. There can be no coincidence!".



The two lines looked at each other very sadly,



"We resemble his non intersecting arms. I guess the circle was right after all"



"Yeah, I guess so".



Right at this moment the old professor resumes his lecture.



"However, if you can construct a projective space that is different from the traditional geometric system, you can create a plane that is part of one infinitely large sphere. Thus every line on the plane will meet whether parallel or not."



"Thus, you can say that the two parallel lines here are brothers on the same plane! ", concluded the professor to the astonishment of the two lines.



Line 1 looks at Line 2 and starts laughing,



"Haha, I knew the old geezer wouldn't betray us!".



"Yeah, he's gonna make us meet at some absurd point yet again!"