brightsky's Noob-tastic Question Thread

[kamil9876]

EDIT: Read this for R²

I highly doubt it, he probably means just like he means instead of .

It is the set of pairs of real numbers so basically your is a function which sends points on the cartesian plane to some points on a cartesian plane. Example: if was rotation by pi/2 anti-clockwise about origin then   (remember rotation matrices, rings a bell?)

[luken93]

EDIT: Read this for R²

I highly doubt it, he probably means just like he means instead of .

It is the set of pairs of real numbers so basically your is a function which sends points on the cartesian plane to some points on a cartesian plane. (example, if was rotation be pi/2 clockwise then  (remember rotation matrices, rings a bell?)

haha, it was the only thing I found and it seemed kinda relevant

[pi]

In the notation , what does the second R mean?
Also with the transformation , what do the first and second R^2s mean respectively?

I always thought referred to the Cartesian plane (real by real). So, would mean transformations in the Cartesian plane?


EDIT: didn't see kamil's post, my bad

[TrueTears]

In general is just the set of all ordered n-tuples

[brightsky]

In general is just the set of all ordered n-tuples

n-tuples?

[pi]

In general is just the set of all ordered n-tuples

n-tuples?

I too was confused...

From wikipedia:

In mathematics and computer science, a tuple is an ordered list of elements. In set theory, an (ordered) n-tuple is a sequence (or ordered list) of n elements, where n is a positive integer.

...

Tuples are usually written by listing the elements within parentheses "( )" and separated by commas; for example, (2,7,4,1,7) denotes a 5-tuple.

[TrueTears]

eg, your cartesian coordinates are all 2-tuples (x,y)

[brightsky]

eg, your cartesian coordinates are all 2-tuples (x,y)

Are there other 'tuples' that aren't associated with axes? It's hard to imagine, say, a 4-tuple, for instance, if that makes sense..

[TrueTears]

The axes you guys relate to 2,3-tuples are just geometric interpretations/functions. The idea of is a concept in its own right, it doesn't need to have any (visible) geometric significance.

[luffy]

I may have completely misunderstood you, but are you referring to dimensions?

For example, 2-tuples will produce a 2-dimensional graph. (i.e. 2 axes)

3-tuples will produce 3-dimensional graphs. (3-axes)

So, in theory, n-tuples would produce an n-dimensional graph? (n-axes)

Or am I completely confused?

[Andiio]

I may have completely misunderstood you, but are you referring to dimensions?

For example, 2-tuples will produce a 2-dimensional graph. (i.e. 2 axes)

3-tuples will produce 3-dimensional graphs. (3-axes)

So, in theory, n-tuples would produce an n-dimensional graph? (n-axes)

Or am I completely confused?

I think you're right, because if we have a 2-tuple, i.e. (x,y) ordered pair, we will naturally have 2 axes (an 'x' axis and 'y' axis) formed along with it.
Not sure if I'm right though

[TrueTears]

I may have completely misunderstood you, but are you referring to dimensions?

For example, 2-tuples will produce a 2-dimensional graph. (i.e. 2 axes)

3-tuples will produce 3-dimensional graphs. (3-axes)

So, in theory, n-tuples would produce an n-dimensional graph? (n-axes)

Or am I completely confused?

Depends on your definition of dimensions, the general definition is that the dimension of a vector space (in this case ) is the number of vectors that make up a basis in that vector space.

Thus we have

There is no such thing that: "n-tuples produce a n-dimensional graph", the italic terms you used are too informal and not precise enough.

The correct way to interpret is that the dimension of the vector space is n.


I suggest you guys just treat it as notation for now and don't worry about the details, you need linear algebra knowledge to understand what I mean. Thinking too deeply at this stage without fundamentals will only confuse you

[luffy]

I may have completely misunderstood you, but are you referring to dimensions?

For example, 2-tuples will produce a 2-dimensional graph. (i.e. 2 axes)

3-tuples will produce 3-dimensional graphs. (3-axes)

So, in theory, n-tuples would produce an n-dimensional graph? (n-axes)

Or am I completely confused?

Depends on your definition of dimensions, the general definition is that the dimension of a vector space (in this case ) is the number of basis in that vector space.

Thus we have

There is no such thing that: "n-tuples produce a n-dimensional graph", the italic terms you used are too informal and not precise enough.

The correct way to interpret is that the dimension of the vector space is n.


I suggest you guys just treat it as notation for now and don't worry about the details, you need linear algebra knowledge to understand what I mean. Thinking too deeply at this stage without fundamentals will only confuse you

Haha - Fair enough. I was just using colloquial language to understand it.

I think you just spiked everyone's interest by the mention of the word "tuples".

Maths gets amazingly repetitive, and so we seek completely new knowledge to satisfy our 'hunger'

[TrueTears]

That's great! I encourage you guys to read further if you have the time. If you are interested to really delve deeper, please take time to read the book, download link is below.

http://www.megaupload.com/?d=E8WXXE2Q

[brightsky]

What's the general idea behind how to prove concurrency using vectors?
More specifically, how do you prove that the medians of a triangle are concurrent?
And from there, how do you prove that the centroid divides each median in the ratio 2:1? (Vectors or an easier way using simple geometry)