My Math Forum The Definition of Length and Width

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 September 13th, 2015, 07:00 PM #1 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry The Definition of Length and Width In most mathematical learning source, it's always defined that the length of a rectangle is its longer side and the width is its shorter one. I thought that the actual definition was length is its horizontal side and width is its vertical side. Now, say that there's a vertical rectangle (the horizontal side is shorter than the vertical side), which one is its length and which one is its width?
 September 13th, 2015, 08:38 PM #2 Math Team     Joined: Jul 2011 From: Texas Posts: 2,922 Thanks: 1518 Really doesn't matter. Use base and height instead.
 September 14th, 2015, 05:25 AM #3 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry It matters because my country's curriculum doesn't accept base and height terms in rectangle. The official terms must be length and width.
September 14th, 2015, 05:39 AM   #4
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 I thought that the actual definition was length is its horizontal side and width is its vertical side.
This is incorrect.

Quote:
 It matters because my country's curriculum doesn't accept base and height terms in rectangle. The official terms must be length and width.

Whilst I agree with skeeter and further comment that any regime that tries to define science by diktat will eventually fail (look what happened to the Soviets) I understand your problem.

Make length the longer side and width the shorter, which ever orientation the rectangle is in.

As as for instance in any introdutory calculus book you will find lots of tall thin rectangles side by side in the introducton to integration.
These books usually talk of the width (shorter horizontal side) and height but you could use length.

What are you going to say to any pupil that sees a foreign book and asks

Why do they do it differently?

 September 14th, 2015, 05:57 AM #5 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry This is a hard case, since the book will be oriented towards Elementary School students.
September 14th, 2015, 07:00 AM   #6
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 Originally Posted by Monox D. I-Fly It matters because my country's curriculum doesn't accept base and height terms in rectangle. The official terms must be length and width.
"Official" terms, huh? Mathematics by fiat.

 September 14th, 2015, 06:24 PM #7 Senior Member   Joined: May 2015 From: Varanasi Posts: 110 Thanks: 5 Math Focus: Calculus Generally you may assume any one either, but as a protocol we consider the longer side as length. Though altering them won't make much difference. Yes its true that normally due to some cognitive habit we all consider the horizontal side as length and vertical one as width. I also used to think similarly when i was in 5 th standard. But then i learned that it wont make any difference. It is some cognitive information that is built in our mind by nature that we think so, it is normal
September 15th, 2015, 12:16 AM   #8
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 Yes its true that normally due to some cognitive habit we all consider the horizontal side as length and vertical one as width.
This is just plain wrong.

Here is a picture of my garden fence.
As you can see it is made of rectangular planks.

Try telling the lumber yard that the long vertical sides are naturally called the width of the plank and the short horizontal sides are called the length and ordering some timber from them.

Or go to a carpet shop and order '5.3m' width of carpet or flooring material off a roll of 'length' 3m.
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September 15th, 2015, 01:22 AM   #9
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 Originally Posted by studiot This is just plain wrong. Here is a picture of my garden fence. As you can see it is made of rectangular planks. Try telling the lumber yard that the long vertical sides are naturally called the width of the plank and the short horizontal sides are called the length and ordering some timber from them. Or go to a carpet shop and order '5.3m' width of carpet or flooring material off a roll of 'length' 3m.
Nice analogy. I think I get it now.

 September 15th, 2015, 01:51 AM #10 Senior Member   Joined: Jun 2015 From: England Posts: 915 Thanks: 271 Although my fence is vertical, many if not most of the examples of rectangles in the real world will have both sides horizontal. Normally we talk of the length of things like rolls of paper, vinyl flooring, planks, metal sections, tubes, ducts, cloth material, roads, railways, .................. ..................and the material or object is of fixed width. We often talk of cutting of a length from the main bulk. Most of the world writes in paper in portrait form (long side up). Sometimes eg rice fields, books, neither the length nor the width is fixed and we designate the length as the longer side. (Incidentally a bit of English you may not know. It is incorrect to use 'longest' to compare only two things. Longest refers to three or more, longer is used when there are only two.) With this scheme you can motivate your pupils with lots of examples from the real world and still keep within your dictator's strictures. They will probably respond better to these examples. Further the ideas of pipes and metal sections leads naturally to other shapes and terms like diameter, radius, and so on.

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