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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,685

A new page for your enjoyment: Parallel and Perpendicular Lines and Planes

Comments, suggestions welcome.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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

Hi MIF;

Very good!

**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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,340

hi MIF,

That's a good page you've got there. How did you get that pencil to stay at an angle to your table?

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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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,685

bob bundy wrote:

How did you get that pencil to stay at an angle to your table?

With my gravity field generator ... doesn't everyone have one?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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

I already knew that so I did not have to ask.

**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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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,695

Hi MathsIsFun,

The page is well made. The illustration is neat! Thanks!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,685

Thanks ganesh!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,340

hi MIF,

With my gravity field generator ... doesn't everyone have one?

Sadly not. Now that would have been very handy for moving the shed. As it was we had to resort to very old technology ... Egyptian I think ... we used rollers.

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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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,685

Rollers are a great invention.

(PS: I never answered your question, sorry. I used Blu-Tack)

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

hi MIF

nice explanation,definitely easier to understand!

I just have to ask which grade is this meant for?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,685

Years 9-12 (Solid Geometry)

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

well this is fine for grades up to 8 but i think a more precise definition would be necessary,because that's how the higher grades learn it.maybe besides what you have you should have a page that explains lines better,if there isn't one already and just give a link to it.i see here that there's one that explains ines on the lower grade level but not the one that gives the real definition of lines by using Euclid's axioms.

EDIT: what i like very much is that you mention that how we draw the line is just our illustration,which is not mentioned that often in other places!

*Last edited by anonimnystefy (2011-11-12 07:52:55)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**reconsideryouranswer****Member**- Registered: 2011-05-11
- Posts: 171

MathsIsFun wrote:

A new page for your enjoyment: Parallel and Perpendicular Lines and Planes

Comments, suggestions welcome.

Click onto this link for the problem (mind bender) at the bottom of the page.

http://www.mathsisfun.com/perpendicular-parallel.html

"Mind Bender

Something that makes my mind bend: we know that if we have two parallel lines,

and we rotate one by 90°, they will be perpendicular to each other, right?

Well, does the same apply to curves? Can you have "perpendicular curves",

by rotating one of them by 90°? I simply don't know, but it is fun to think about."

---------------------------------------------------------------------

Let there be two racetrack-shaped closed curves,

not necessarily the same width or length, having

semicircles at each end facing out and each semicircle

is connected by parallel lines to the endpoints of the

respective semicircles.

Let these two curves be oriented parallel to each other,

have sufficiently long line segment sides to connect

the semicircles, and be positioned relative to each other

so that when one is rotated 90 degrees, there will be

either two intersection points or four intersections where

the intersecting sides will be perpendicular to each other.

Before the rotation of 90 degrees, there are cases where

one of these "racetrack" curves might even be completely

inside of the other.

Signature line:

I wish a had a more interesting signature line.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,685

Interesting example, thanks.

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