Math Is Fun Forum

redheadcaliforniagirl

Member

Registered: 2014-09-17

Posts: 1

How to name a plane

What other ways can you name a plane? Thanks (:

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: How to name a plane

What kind of plane? The one that flies or the one in geometry or the tool?

For the one that flies over my house all night long:

http://www.thesaurus.com/browse/airplane

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: How to name a plane

hi redheadcaliforniagirl

Welcome to the forum. 

As this is a math website, I'm gunna guess you mean in geometry.

Two lines that cross will make a plane.  If the directions of those lines is given by vectors a and b, and they cross at a point with position vector c, then the equation of the plane is:

where lambda and mu are variable scalars.

In fact this equation will define a plane if c is in the plane and a and b are any vectors in the plane.  (but come to think of it, that means they will cross somewhere.  So what I'm really trying to say is that c doesn't have to be the crossing point; just any point in the plane.)

In Cartesian terms this can be shown to be equivalent to:

It can also be shown that

is perpendicular to the plane so yet another form for the plane is

where n is a vector normal to the plane and s is a constant.

That's all I can think of for the moment, but I'm sure there are more.

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: How to name a plane

How do you define a plane in spherical geometry?

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“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
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Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: How to name a plane

hi Stefy,

Well, personally, I don't.  As the surface of a sphere is not flat, I wouldn't try to find such a thing.

In 3D geometry, any plane has 'two degrees of freedom'.  That's what lambda and mu do.  They can be independently chosen.  A line has just one degree of freedom.

On the surface of a sphere, the surface has two degrees of freedom already:

You can (with some restrictions) choose say x and y, but then z is determined.

So if you are determined to define a plane in spherical geometry, I suggest its the entire surface. 

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: How to name a plane

But, if we are looking at 3D space, spherical geometry wouldn't be placed on the surface of a sphere, but rather on the surface of a hypersphere.

Also, after your post I realised that I wanted to say "in polar coordinates". But this way it's more interesting.

Last edited by anonimnystefy (2014-09-17 06:29:41)

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“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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: How to name a plane

Oh right.  4D space.  That should have been obvious. 

Poor redheadcaliforniagirl.  This may be more than she wanted.

I'll give it some thought, but you may have to wait for her input first.

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

SolarDevil

Member

Registered: 2014-09-14

Posts: 37

Re: How to name a plane

The plane in geometry is mainly defined with 3 points on the plane.

Solar

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