Is a Square a Rectangle?Date: 06/04/97 at 07:43:43 From: Kathy Harris Subject: Elementary geometry Dear Dr. Math, We are studying geometric shapes in my second grade classroom. If you could answer this question in terms that they can understand, I would greatly appreciate it. Is a square a rectangle? Also, what is a pentagon? In our studies we have found books with conflicting information and would like your ideas. Thank you! Kathy Harris Date: 06/04/97 at 12:14:43 From: Doctor Ceeks Subject: Re: Elementary geometry Hi, The definitions of certain things in math sometimes become arbitrary and depend on conventions. Different people will feel different ways about things. When there is conflicting information, it's okay to discuss things and try to come to some agreement within your class as to which definitions are the happiest ones to use. My personal feeling on the questions you asked are as follows: A square is a special kind of rectangle. I like to consider the square as a special kind of rectangle because I've often had to refer to all shapes with four sides and four right angles as rectangles. If the rectangle were defined to not include the square, I would have to say "rectangles and squares" whenever I wanted to refer to such shapes. It's less cumbersome to allow "rectangle" to also refer to squares so I can simply say "rectangles" when I want to refer to such shapes. Also, of all rectangles, the one with four equal sides has the special property that all its sides are equal, and for this reason, has warranted a special name, "square". Some people will want to disagree and not allow rectangle to include squares because maybe when they say "rectangle" they really want people to think of something with a length and a width. This is fine, if they want to think that way. When I want to refer to a non-square rectangle, I might say "non-square rectangle" or "generic rectangle". Anyway, the whole business is not really worth arguing about once it is seen that of all the four sided figures with four right angles, there is a special one which also has four equal sides. That's worth noting, and once noted, it's time to move on to more important things. A pentagon is generally agreed upon to be a five sided figure. When people want to refer to the special pentagon that has five equal sides and five equal angles, they say "regular pentagon". -Doctor Ceeks, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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