Parallelism and Concentric Circles ```Name: Chris Status: student Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: Parallel lines. I was playing with a lock in geometry class on day and my teacher asked me if the outside line and the inside line of the lock are parallel. said that it was, but he told me that it could not be, but he never gave me a reasonable explanation. I think that the inside and outside lines could in fact be parallel. Could you please give me an explanation as to why they are not considered parallel? Everything I have looked up about them never says anything about the lines not being able to curve like that in an arch. Replies: By definition, parallel lines must be straight lines in the same plane. So even though the lines do not intersect, they are not parallel. Scott P. Smith Lines are, according to Wikipedia, perfectly straight. This coincides with the idea that equations of lines are of the form ax + by = c or the possibly more familiar y = mx + b (slope - intercept form). So your teacher is correct. Two arcs that never meet, your lock hasp, would be considered concentric - that is they have a common center but different radii. Concentric arcs never meet either. It may seem like semantic games, but the field of mathematics is one for rigid and precise definitions within a strict logical and semantic framework. Mathematics is often in the forefront of human thought and deals with questions that are so "far out" they may not be obviously tied to the "real world". The way a mathematician can be sure they are correct is if other mathematicians can follow each and every step of their argument and find no "holes" or logical errors. Thus they are extremely precise and tend to break things down into a series of steps, each of which has its own proofs. That being said, there is very little mathematics out there that has NOT be applied to other problems once technologists and other scientists get hold of it. So if math seems a bit over precise, cut it some slack. We all benefit from the work mathematicians do and have done. Robert Avakian Chris, The answer does in fact depend on what you mean by parallel. In the strictest sense, a line does not curve. Parallel lines must be in the same direction everywhere. The curves are only parallel at the closest points. The top of one circle is not parallel to the left side of the other circle. In some areas of science and engineering, the term parallel can be used in a variety of ways. One refers to two paths that are identical but offset. Two circles of the same size but with different centers would qualify. Another use refers to two paths that always maintain the same distance from each other. Closest points between the paths always have the same distance. In this case, concentric circles are parallel. Objects traveling along parallel lines will always be moving in the same direction as each other. Objects traveling along concentric circles only maintain same directions if they are both traveling at the same number of revolutions per second. Dr. Ken Mellendorf Click here to return to the Mathematics Archives

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