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## #1 2011-11-08 17:55:13

MathsIsFun
Registered: 2005-01-21
Posts: 7,687

### Parallel and Perpendicular Lines and Planes

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

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

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## #2 2011-11-08 18:58:06

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

### Re: Parallel and Perpendicular Lines and Planes

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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## #3 2011-11-08 20:02:17

bob bundy
Registered: 2010-06-20
Posts: 8,462

### Re: Parallel and Perpendicular Lines and Planes

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #4 2011-11-09 11:22:13

MathsIsFun
Registered: 2005-01-21
Posts: 7,687

### Re: Parallel and Perpendicular Lines and Planes

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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## #5 2011-11-09 11:56:14

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

### Re: Parallel and Perpendicular Lines and Planes

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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## #6 2011-11-09 23:57:46

ganesh
Registered: 2005-06-28
Posts: 27,057

### Re: Parallel and Perpendicular Lines and Planes

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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## #7 2011-11-10 10:43:24

MathsIsFun
Registered: 2005-01-21
Posts: 7,687

### Re: Parallel and Perpendicular Lines and Planes

Thanks ganesh!

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

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## #8 2011-11-10 20:39:58

bob bundy
Registered: 2010-06-20
Posts: 8,462

### Re: Parallel and Perpendicular Lines and Planes

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #9 2011-11-11 10:33:04

MathsIsFun
Registered: 2005-01-21
Posts: 7,687

### Re: Parallel and Perpendicular Lines and Planes

Rollers are a great invention.

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

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

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## #10 2011-11-11 11:28:42

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Parallel and Perpendicular Lines and Planes

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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## #11 2011-11-11 15:52:45

MathsIsFun
Registered: 2005-01-21
Posts: 7,687

### Re: Parallel and Perpendicular Lines and Planes

Years 9-12 (Solid Geometry)

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

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## #12 2011-11-12 07:51:30

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,039

### Re: Parallel and Perpendicular Lines and Planes

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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## #13 2011-11-25 16:59:00

Member
Registered: 2011-05-11
Posts: 171

### Re: Parallel and Perpendicular Lines and Planes

MathsIsFun wrote:

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

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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## #14 2011-11-26 10:08:22

MathsIsFun
Registered: 2005-01-21
Posts: 7,687

### Re: Parallel and Perpendicular Lines and Planes

Interesting example, thanks.

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

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