Segmenting PathsDate: 08/20/98 at 19:23:58 From: Amber Subject: Geometry points, lines, and planes The question says: A path between opposite vertices of the square is made up of hundreds of horizontal and vertical segments. What is the best approximation to the length of the path - 24, 34, 44, or more than 44? It has a diagram of a box with 17 on top, bottom, and both sides, with steps going up to the top of the box. Do you think that you can help me figure this problem out? I don't know how to get started. Date: 08/21/98 at 13:17:26 From: Doctor Peterson Subject: Re: Geometry points, lines, and planes Hi, Amber. This is a good thinking question. One way to think about it is to picture a simpler case, then see how things would change if you had hundreds of segments. Here's your square with just one horizontal and one vertical segment making the path: 17 +----------------+ | | | | | | | | 17 | | | | | | +----------------+ How long is that path? (It's supposed to be right along the top and right edges of the square.) It should be 17 + 17, right? Now let's break it up into four pieces: 6 +------+---------+ | | | | 10| | | | | | | 11 | | +---------+ | |7 | | +----------------+ How has the length changed? Now it's 6 + 10 + 11 + 7. Now what happens if we keep on breaking it up into smaller segments? +---+------------+ | | | | | | | +--+ | | | | | +----+ | | | | | | | +-----------+----+ This should give you an idea how to answer the question. - Doctor Peterson, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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