Math Is Fun Forum

Andrea11

Member

Registered: 2011-08-26

Posts: 1

Double size of shape

At school today my daughter was asked to double the size of a shape by puting a x at the top or the square at the top then havin " make it to times biger bt counting alopng how many away it was from point x could you help me to xplain this to her because she does not get it ? thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Double size of shape

Hi Andrea11;

Got a drawing or a link with a picture?

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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Double size of shape

My Mom and I have talked about this doubling or halving of the size of a photograph recently.
It is interesting because there is no consensus for regular non-math people on what
half or double the size of something really even means.    Because there are different
ways to measure something such as the height, the width, a diagonal, the height times the
width which is the area, or the volume or weight of something.  The square root of 1/2 and
the cube root of 1/2 are useful numbers in this discussion, when comparing the x, y,  or
z linear dimensions with the area or volume shinking by half.

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anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Double size of shape

hi John

i finally get to talk to you.when i am online you never are!

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reconsideryouranswer

Member

Registered: 2011-05-11

Posts: 171

Re: Double size of shape

My Mom and I have talked about this doubling or halving of the size
of a photograph recently.  It is interesting because there is no
consensus for regular non-math people on what half or double the
size of something really even means.

Take it in context.

If you double the size of a line segment, its length is doubled.

A circle, rectangle, or a photograph's size is its area.  For
a rectangle, only one dimension (the width or the length)
need be doubled to double the size of the rectangle. 
However, if each of the two dimensions of the rectangle is
doubled, its size is quadrupled.

A sphere and a rectangular box's size, for instance,
are their volumes.  If exactly one of the dimensions
of the box (width, length, or height) is doubled, then
the size of that box (its volume) is doubled.

However, if each of the three dimensions (of the box)
is doubled, then the volume of the new box is eight
times the volume of the original box's volume.

Regarding the Moon, it is approximately spherical.
Its size is its volume.

However, when someone speaks of the apparent
size of a full Moon looking larger than at other times,
they are looking at a shape which is circular (an area). 
Then, they should not be meaning the actual Moon's
radius or circumference (linear dimensions), and they
should not be meaning the actual Moon's volume,
which is cubic.

When the full Moon's size is said to appear larger,
then the area of the circular side showing should
be what is meant.

** The Moon may appear larger to some people when
viewed from the horizon versus elsewhere in the sky
from visual cues near its image on the horizon,
versus being well above the horizon.

Last edited by reconsideryouranswer (2011-08-28 06:48:13)

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Double size of shape

hi Andrea11

Have a look at my picture below.  This shows what is meant.

You can start with any shape.

X can be anywhere (although if it's too far from the shape you may end up off the paper).

You count how far across and up it is to each point of the shape.  I've just shown one point that is 2 across and 7 up.

You go the same amount again ( 2 across and 7 up ) to get to the new point of the enlarged shape.

I've shown the across and up as if you had counted from X (so 4 across altogether and 14 up).

The new shape is an exact copy but twice as big.

You can go three times as far to treble the shape, and so on ....

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

reconsideryouranswer

Member

Registered: 2011-05-11

Posts: 171

Re: Double size of shape

.

The new shape is an exact copy but twice as big.

Bob

 

The following is a case where the new shape is twice as big as the original shape:

Suppose you have a rectangle with dimensions of

If each dimension is multiplied by

then the new area is doubled.  That is, you have a shape
twice as big.  Or double only the width, and you have the same result.  Or double only the length, and you have
the same result.  There are an infinite number of ways to achieve this.

However, (again i'm repeating myself from my other post), if the width *and* the length are doubled, then the shape
will be four times as big.  This means the area has been quadrupled.

Last edited by reconsideryouranswer (2011-08-29 06:32:32)

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Re: Double size of shape

The Tale of Mr Big.

Oh, I'm so sorry to make such a big mistake.  I never wanted to mislead anyone.

The trouble is, when I went out to buy a dictionary I thought I'd been so clever by getting a pocket book; such a big saving when I hadn't much cash.

So I decided to go down town to the big library.  Now why do they call it that?  Is it because the buildings cover 5 acres?  Or because it's 5 storeys high.  Or maybe it's because of the 27 separate rooms, all full of books.  Personally, I think it's because it has over a million books.

I went up to the librarian.  She won't be working there for much longer as she is big with child. 

"I want a big dictionary", I said.

"Well all the dictionaries are up there on the big shelf", she replied, pointing at the biggest shelf of books I've ever seen.  "Do you mean big as in heavy?  That red one weighs over 5 pounds.  Or big as in tall, for that blue one is the tallest on the shelf.  Or perhaps you want the one with the most words, in which case 'The Big Book of Words' is the one for you."

"Well, I was rather hoping for one that has the biggest area",  I said, beginning to sound somewhat unsure of myself.

"Nope, never heard of that", she said.  "You'd better take down The Big Book of Words if it's a meaning you're after."

I went over to the big shelf.  There was a ladder lying against the wall.

"No, not that ladder, it'll be too small", she warned.  "Go round the corner and get the big ladder".

So I did.  It was a long climb up to the shelf, and I staggered back to a desk with my book.  It had a big space devoted to all the meanings of the word 'big'.  It said 'Of great or considerable size, height, weight, number, power or capacity'.

"Oh no", I thought, "that's really done my head in.  No mention of area at all!" 

All that cycling and climbing ladders and carrying heavy books had left me short of blood sugar.  So I went next door to the sweet shop and bought a big bar of chocolate! 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob