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#1 2016-10-14 05:44:33

samuel.bradley.99
Member
Registered: 2016-03-16
Posts: 51

Change of shape

How can we transform a parallelogram with sides n and 1.1*n into a rhombus of equal area, just by one cut?

Last edited by samuel.bradley.99 (2016-10-14 06:21:56)

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#2 2016-10-14 05:48:55

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Change of shape

Hi;

Equal surface? What does that mean?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2016-10-14 06:02:34

zetafunc
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Registered: 2014-05-21
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Re: Change of shape

Maybe he means equal area.

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#4 2016-10-14 06:23:01

samuel.bradley.99
Member
Registered: 2016-03-16
Posts: 51

Re: Change of shape

Exactly, I corrected the wording. Sorry guys but English is not my mother tongue!!

zetafunc wrote:

Maybe he means equal area.

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#5 2016-10-14 19:49:23

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Change of shape

Only in certain cases it can be done.If one of the diagonals has the dimension of a side either n or 1.1 n ,it can be cut along that diagonal and pasted on the other side.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
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#6 2016-10-14 20:57:21

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,153

Re: Change of shape

hi samuel.bradley.99

PTUuegn.gif

This works only if A lies on that circle.  Still working on a general case.

AB = DC = 1.1n

AD = BC = n

Note AC = n, so the dotted diagonal will make the cut.  Translate ADC (ie. Move it maintaining the parallel directions)  so that DC fits over AB as the new diagonal. 

The new parallelogram has four equal sides of size n, so it is a rhombus.

Bob


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

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#7 2016-10-16 02:15:47

samuel.bradley.99
Member
Registered: 2016-03-16
Posts: 51

Re: Change of shape

Thank you, but how about in the general case, where we don't know whether A lies on the circle?

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#8 2016-10-17 07:17:55

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,153

Re: Change of shape

hi samuel.bradley.99

General solution:

OmZYmsb.gif

Draw parallelogram ABCD where AB = 1.1n and BC = n

With centre D and radius 1.1n, draw an arc to cut AB at E.

The cut required is along the line DE.

Remove the triangle coloured yellow, and move it to the position shown in orange.

AB = DC = EF = FC = 1.1n so EFCD is the required rhombus.

Bob


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

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#9 2016-10-18 01:32:07

samuel.bradley.99
Member
Registered: 2016-03-16
Posts: 51

Re: Change of shape

Guys you are geniuses! Respect!!
Thank you so much!!

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