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#1 Re: Help Me ! » Strange Sequence » Yesterday 23:48:15

So p > 1.

We can directly get this from (ii) in the problem statement.

How does the conclusion help, though?

#2 Re: Help Me ! » difference of zero, circle and alphabet O » Yesterday 19:44:47

According to your definition, the zero sphere is in R.

I'd rather have the zero sphere to be the trivial sphere {0} in {0} and 1-sphere in R.

#3 Re: Help Me ! » Strange Sequence » Yesterday 19:42:46

The email ends with asking me to find all possible values of log_2015(a[2015]) - log_2014(a[2014]) which would be 0 in these cases.

#4 Re: Help Me ! » Strange Sequence » Yesterday 19:08:05

Is that the only possible solution?

#7 Re: Help Me ! » Strange Sequence » Yesterday 12:19:31

What should I be using as k?

#9 Re: Help Me ! » difference of zero, circle and alphabet O » Yesterday 05:04:15

Why'd you want to define it as the points in n+1 space instead of n-space?

All we need now is for bobbym to provide a deforming procedure in geogebra.

I created a deformation in geogebra:
dMYVUTO.gif

#10 Re: Help Me ! » difference of zero, circle and alphabet O » Yesterday 04:23:40

I think an n-sphere is defined to be the set of all n-points in n-space that is equidistant from a fixed point.

#11 Re: Help Me ! » Sphere packing » Yesterday 04:07:24

Thanks, the same trick worked again.

#12 Re: Help Me ! » Sphere packing » Yesterday 04:05:39

Oh, yes. That works.

Now I need to do the same thing for a 2014-dimensional hypersphere.

#13 Help Me ! » Strange Sequence » Yesterday 03:48:02

Agnishom
Replies: 12

Somebody emailed me this problem:

How many such sequences are there such that
(i) a[m*n] = a[m]*a[n] and
(ii) for every m < n, a[m] < B*a[n] for a positive constant B?

The only solution I have so far is the sequence a[n] = n

#14 Re: Help Me ! » Sphere packing » Yesterday 03:02:17

In the same way, AD should be just sqrt(3). Is it?

#16 Re: Help Me ! » Sphere packing » Yesterday 00:11:34

bob bundy wrote:

The length CD appears to be  √2.r but the true length will be longer in the ratio AD:AB.

I think it should be sqrt(3)*r

Then you can form an equation for r using AD = AB + BC + CD

Bob

How do we get information on CD?

#17 Help Me ! » Sphere packing » 2014-12-15 20:12:27

Agnishom
Replies: 6

We have a cube of side 2, inside which a sphere or radius 1 is inscribed. What would be the radius of the sphere that would have been inside the cube touching the central sphere and the three walls of the cube?

#18 Re: Help Me ! » difference of zero, circle and alphabet O » 2014-12-15 03:01:23

bob bundy wrote:

hi zetafunc.

Excellent!  All we need now is for bobbym to provide a deforming procedure in geogebra.

Bob

That is hardly nexessary.

We can truly experimentally prove the existence of the homeomorphism with a soft rubber ball smile

#19 Guestbook » Rebuttal on the continuum - A Green Messageboard » 2014-12-14 21:13:17

Agnishom
Replies: 0

Hi  John Green;

I am afraid your conception of 16 year olds is not perfect.

I am 14 and I realise that f(n)=2n  does a very good job of bijecting [0,1] to [0,2] which would pretty much imply the same cardinality.

I do not mean to say that there is no truth in your reasoning about kids. You are sort of correct about abstract reasoning but 16 is a little too old. 12 would be okay.

I'd have used the concepts of Aleph-Null and Aleph-One to explain my significant other on different sorts of infinities. Hilbert's hotel is even better.

By the way, do you think that there exists a set whose cadinality is strictly between that of natural numbers and reals.

#20 Re: Help Me ! » number of solutions to a linear equation » 2014-12-14 07:09:58

gourish wrote:

I bet bobbym is a professor isn't he?

The person below will tell.

#21 Re: Help Me ! » number of solutions to a linear equation » 2014-12-14 06:59:13

bobbym wrote:

That is what they say. The last person to say that was?

Zeilberger wrote:

I agree with G.H. Hardy that mathematics is a young man's game (except for the "man" part), but "young" does not mean "under thirty", and not even "under forty". "Young" means, "young at heart", and willing to learn new things and new methodologies and master new technology. If you will follow my advice, I am sure that you would achieve much more than your already very impressive (albeit mostly boring) feats, and your future achievements will not only be technically challending, but also exciting, not just to you and to your thirty cronies, but to all of us common folks.

#22 Re: Help Me ! » number of solutions to a linear equation » 2014-12-14 06:46:28

This note can provide some help finding the book on the web

Hahahha, thanks! Professors are not the only ones having beards, though.

Mathematics is a young man's game.

#23 Re: Help Me ! » number of solutions to a linear equation » 2014-12-14 06:37:31

gourish wrote:

okay... well it says that the book is for B.Sc in math... i am kid in 12th grade... you think it's the right book for me?

Did you know I am in the 11th standard?

#24 Re: Help Me ! » number of solutions to a linear equation » 2014-12-14 06:31:34

Graph theory is a part of combinatorics.

Rewind your life back to Class XI. You would not have believed that solutions to x+y+z=10 is combinatorics. Would you? You'd have thought it is algebra.

In the same way, you probably do not see yet why graph theory is a part of combinatorics, but you'll later.

#25 Re: Help Me ! » number of solutions to a linear equation » 2014-12-14 06:20:24

Yes, it provides a very strong base for combinatorial reasoning. That is better than books with around 100-200 problems with just 4-5 line solutions without any explanation

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