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Do you know how to add algebraic fractions? For example try this:
1/m + 1/n
If not, ask and I can explain it.
I wonder if the ancient Babylonians played base-60 Sudoku ....
You need to add the two fractions:
find the common denominator!
the process is the same as this process for adding fractions with 'ugly denominators':
3/23 + 7/57 is:
3 * 57 + 7 * 23
--------------------
23 * 57
Does that help?
Glad to help!
I like doing the hexodoku. It helps me learn the language base by heart a little more.
sounds like fun
@ espeon - I don't think you'll ever need to know about hex and bin and oct unless you take Computer Science courses at some point or want to study computers or electrical engineering or something closely related.
But if you want to learn them just for fun, I can try to explain more. just ask!
I was going to add Knot Theory, but it seems even that has applications! (see http://en.wikipedia.org/wiki/Knot_theory)
Does knot!
hah.
But as for Group theory, I believe it has applications in General Relativity, although that is just by reading it somewhere. And being very technical, group theory is involved in Galois theory which is extremely important when talking about the roots of polynomials of degree 5 or greater. But again, that would probably go under Galois theory rather than Group theory. Kind of hard to draw the line though.
Thanks, I'll need to read up on those topics!
We use "base 10 numbers" because we use 10 digits: 0 to 9.
And when we count we start a new column after we get past 9 to 10, and start counting starting with 1 in that column again:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
.. but thats not the only way it can be done! In Hex (hexadecimal) numbers we use 16 different digits, so when we count 7, 8, 9, ... we dont start another column and write 10. We use the letters A, B, C, D, E, F *as digits*. We only start a new column when we get to the digit F. The digits A to F have the values 10 to 15: A means 10, B means 11, and so on.
So counting in hex goes like this:
1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21, ....
Notice that once we pass 'F', we have to start another column just as in regular decimal number counting.
Put your calculator into "hex mode" and try 1 + 9, 2 + 9, 3 + 9 and see what happens!
But: why would anyone do this? Well, its important for storing numbers inside computers. But thats a large topic.
1.10^2
2.10^3
3.10^5
Right!
You have just calculated some logarithms.
The logarithm is the number of times the number called the *base* has to be multiplied by itself to get a certain number as a result. Or in other words, what power of the base gives a certain number. The base in this case was 10.
the notation is like this ('log' is short for logarithm):
10^2 = 100, so we say log(100) = 2.
10^3 = 1000, so we say log(1000) = 3.
10^5 = 100000, so we say log(10000) = 5.
Try the "log" button on your calculator for numbers like 100000, 10000000, etc.
if u havent noticed im much smarter than other 12 year olds
I would say so!
Thanks to everyone for the nice welcome.
Hi polylog,
Yet, as a piece of information, polylog is undefined,
thats because if you repeatedly take the logarithm of a number,
at some stage you reach either zero or a negative number.
Thereafter, logarithm of that number is undefined or meaningless
Anyways, it was a lovely thought to chose this username.
Actually I can't take any credit for coming up with the name... I just remembered it from an article about "integrals that can and cannot be done" from Wolfram Research, and the Polylogarithm function (PolyLog[n, z]) was one of the special functions that comes up with along with other integrals that have no elementary antiderivatives, like the functions erf(x), the log integral Li(x), and so on.
Here is a good definition: http://mathworld.wolfram.com/Polylogarithm.html
hi polylog also ganesh whats a logarithm?
hi espeon, here is a simple introduction to the idea:
Consider multiplying 10 *by itself* twice: 10 x 10 = 100.
Or 3 times: 10 x 10 x 10 = 1000.
Or 4 times: 10 x 10 x 10 x 10 = 10000
Now, try to answer these questions:
"How many times do we multiply 10 by itself to get 100?"
"How many times do we multiply 10 by itself to get 1000?"
"How many times do we multiply 10 by itself to get 100000?"
Number theory in cryptography is a great example. The security of online banking for example would not be possible without the RSA encryption algorithm which is based on number theory!
Image processing in software like Photoshop, for example compression and various image effects, require advanced topics like Fourier analysis and Wavelet analysis (a very complicated topic).
For example the new JPEG 2000 format for internet images is based on Wavelets. Here is some info:
http://en.wikipedia.org/wiki/Wavelet
http://en.wikipedia.org/wiki/JPEG_2000
Fractals are another advanced math topic with lots of applications. Here is a nice list of these:
http://library.thinkquest.org/26242/full/ap/ap.html
And of course a great deal of advanced mathematics is used in engineering, for example Partial Differential Equations, Tensor Calculus (e.g. in fluid dynamics), and some Complex Analysis (in circuit analysis).
As for purely theoretical math.. well I have so far never seen any applications of Group Theory for example. But it probably does...
I was going to add Knot Theory, but it seems even that has applications! (see http://en.wikipedia.org/wiki/Knot_theory)
I just wanted to say hello to everyone on this great forum.
I've been reading a lot of the old posts looking for interesting problems and enjoying them all.
I hope to learn a lot and also contribute whenever possible. Thank you for your time