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Thread: Need help understanding the mathematics mentioned in a popular science book

  1. #1
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    Question Need help understanding the mathematics mentioned in a popular science book

    The text is this, quoted:

    "Well, you know how you can figure the distance between two points by measuring the distance along two parallel axes, right? If an object is three steps east of you and four steps north, then it's five steps away in a direction 37 degrees east of north. That total distance of five steps will be the same, no matter how you orient your coordinates."

    I think he is discussing conversion from cartesian to polar coordinates but I'm not sure what he means by parallel axes. Can someone explain?

    This is from: How To Teach Relativity To Your Dog, by Chad Orzel, page 95.

    thanks
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  2. #2
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    Re: Need help understanding the mathematics mentioned in a popular science book

    I think this is a typo. He clearly meant perpendicular axes, not parallel.
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  3. #3
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    Re: Need help understanding the mathematics mentioned in a popular science book

    First, Halls is right about the typo. But just correcting the typo may not elucidate what is being said. What is being said is that if the x and y axis are rotated around the origin, the co-ordinates of the point will change, but not the length of the line between the point and the origin. In this case, length from a point to the origin is invariant with respect to rotation of the axes around the origin.
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