Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
#351 Re: Help Me ! » why mathematical induction works? » 2006-07-22 04:02:39
It's interesting that the induction is so foundamental, that it can't be proved or disproved using only non-induction methods. It's axiomatically true. It's the fifth of the Peano's axioms:
http://en.wikipedia.org/wiki/Peanos_axioms
#352 Help Me ! » Wanted ... a function » 2006-07-22 03:57:08
- krassi_holmz
- Replies: 6
Hi.
I need a function, which has the property:
Thank you.
#353 Re: This is Cool » Hypobola functions to Sine and Cosine functions » 2006-07-22 03:29:56
And...
Don't forget the great equation:
#354 Re: This is Cool » pi and other numbers with infinite numbers of decimals » 2006-07-22 03:22:26
Such numbers are called normal.
Here is it: (I'm not explaining because the explanations are there):
http://en.wikipedia.org/wiki/Normal_number
#355 Re: This is Cool » pi and other numbers with infinite numbers of decimals » 2006-07-22 03:19:48
Interesting question.
It may be extended for another numbers, such as e, phi, sqrt(2), ect.
Last month I read about this theme.
I'll post a link with information.
#356 Re: Help Me ! » the area of the square and rectangle » 2006-07-22 03:14:05
It's simple:
Let the rectangle is ABCD and it's diagonals intersect in E.
Then S(ABCD)=S(AEB)+S(BEC)+S(CED)+S(DEA).
Now use that S(XYZ)=xy sin Z and apply to all triangles.
#357 Re: Help Me ! » Row reduced echelon form » 2006-06-13 22:54:18
And the gaussian reduction can be use not only with square matrixes.
#358 Re: Help Me ! » Row reduced echelon form » 2006-06-13 22:53:08
I'm new to this, but I have a feeling that every matrixes can be reduced.
And this is useful for calculationg the determinant:it is equal to the porduct of the diagonal elements:
for the example, det A=1.1.-8=-8.
#359 Re: Help Me ! » Row reduced echelon form » 2006-06-13 22:49:03
Starting up, in every row eliminate one more element.
#360 Re: This is Cool » Geometric probability » 2006-06-13 21:34:48
But here's what's happening when we restrict the space:
If we have a square with langth, say 1, and a circle in this square, then the probability a point, at random, to be in the circle is the area of the circle. But the amont of points in and out the circle is infty. Why? When you can define the probability as some measure over the space?
#361 Re: Help Me ! » Please Help! » 2006-06-13 21:20:08
Want to see Mathematica? Here is it (direct approach):
#362 Re: Help Me ! » Please Help! » 2006-06-13 21:17:22
By the way, here's how I came up with my solution:
sqrt(4 + sqrt(4 + sqrt(4-x))) = x
Therefor:
4 > x > sqrt(4 + sqrt(4))
4 > x > sqrt(6)
(*)4 > x > 2.4The original equation can be written as:
-140 - x + 192x^2 - 88x^4 + 16x^6 - x^8 = 0By factorizing it we get:
-(x^2 + x - 4)(x^3 - 2x - 3x + 5)(x^3 + x^2 - 6x - 7) = 0
It's not that easy:
-(x^2 + x - 4)(x^3 - 2x - 3x + 5)(x^3 + x^2 - 6x - 7)=-140 + 55 x + 170 x^2 - 68 x^3 - 72 x^4 + 22 x^5 + 14 x^6 - 2 x^7 - x^8
So, wrong factorisation.
#363 Re: Help Me ! » Please Help! » 2006-06-13 21:11:23
But everything which can be done with the one, can be done and with the other (even the plotting in Mathematica, but it requires little more code than in Maple)
#364 Re: Help Me ! » Please Help! » 2006-06-13 21:09:27
Agree.
#365 Re: This is Cool » Geometric probability » 2006-06-13 04:16:40
An infinitesimal value.
I THOUGHT THE SAME THING!!!
#366 Re: Help Me ! » please help with RADICALS! » 2006-06-13 02:45:17
wildcats, sometimes, being approximate isn't good enough. For an engineer, it usually is. This is why we (or at least I) hate them.
Hate who???:P
#367 Re: Help Me ! » Simplifying an Expression » 2006-06-13 02:43:37
For the cubic equation, I don't think it will help, but here are the exact answers ( I bet you didn't thought this ):
m=-\sqrt{\frac{1}{2}-\frac{1}{8} \sqrt[3]{\frac{1}{38} \left(11+21 i \sqrt{3}\right)}-\frac{1}{8} i \sqrt{3} \sqrt[3]{\frac{1}{38} \left(11+21 i
\sqrt{3}\right)}-\frac{1}{4 2^{2/3} \sqrt[3]{\frac{1}{19} \left(11+21 i \sqrt{3}\right)}}+\frac{i \sqrt{3}}{4 2^{2/3} \sqrt[3]{\frac{1}{19} \left(11+21 i
\sqrt{3}\right)}}}\lor m=-\sqrt{\frac{1}{2}-\frac{1}{8} \sqrt[3]{\frac{1}{38} \left(11+21 i \sqrt{3}\right)}+\frac{1}{8} i \sqrt{3} \sqrt[3]{\frac{1}{38}
\left(11+21 i \sqrt{3}\right)}-\frac{1}{4 2^{2/3} \sqrt[3]{\frac{1}{19} \left(11+21 i \sqrt{3}\right)}}-\frac{i \sqrt{3}}{4 2^{2/3} \sqrt[3]{\frac{1}{19}
\left(11+21 i \sqrt{3}\right)}}}\lor m=\sqrt{\frac{1}{2}+\frac{1}{4} \sqrt[3]{\frac{1}{38} \left(11+21 i \sqrt{3}\right)}+\frac{1}{2 2^{2/3} \sqrt[3]{\frac{1}{19}
\left(11+21 i \sqrt{3}\right)}}}#368 Re: Help Me ! » Simplifying an Expression » 2006-06-13 02:41:55
For the cubic equation, I don't think it will help, but here are the exact answers ( I bet you didn't thought this ):
#369 Re: Help Me ! » Please Help! » 2006-06-13 02:25:05
You solved it using Maple (or any other math software out there), didn't you?
I already solved the equation myself, but my teacher complains about my answear being long and ugly. (Containing cosines and arc-cosines and stuff.)
Yours looks better.
What does 'i' stand for?
Stas B. wrote:You solved it using Maple (or any other math software out there), didn't you?
I already solved the equation myself, but my teacher complains about my answear being long and ugly. (Containing cosines and arc-cosines and stuff.)
Yours looks better.
What does 'i' stand for?Maple and Mathematica, which is better? How do you feel about it guys??
In Plotting, I really support Maple.
I agree Maple is better in plotting sometimes... 
Or maybe just I can't "draw" good...
I'm for Mathematica
Here are some Mathematica results (by me, in this forum):
Search
#370 Re: Help Me ! » Permutation » 2006-06-10 21:16:35
I don't know... I get 1300...
#371 Re: Help Me ! » A problem. » 2006-06-10 21:13:30
2) substitute with 0 and solve for t.
#372 Re: Help Me ! » Master Sum » 2006-06-10 21:12:22
Good.
How?
#373 This is Cool » Geometric probability » 2006-06-10 06:31:46
- krassi_holmz
- Replies: 5
What is the probability a random quadrangle to be inscribed (described) in a circle?
#374 Re: This is Cool » Question about Infinity » 2006-06-10 06:26:54
It can be anything!!!
It is well-defined "undefinity".
(We can assume that there exists an "object" undef, such that by definition: n/0=UD; inf-inf=UD ect.)
We have 0,inf,und (undefined) Here's a system of definition rules:
inf - inf := und;
inf / inf = 0 / 0 := und;
inf / 0 = 0 / inf := und;
inf * 0 := und;
und +-*/ all others :=und;#375 Re: Help Me ! » Permutation » 2006-06-10 06:11:50
Help:
It is greater than 100.
