Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
#1376 Re: This is Cool » The Shape of a Suspension Bridge's Main Cable » 2006-04-06 13:29:25
But if we had a bridge that had only one hanger that was planar across the entire main cable, then it would be parabolic.
Yes, you could say so. but to be exact, near. because matter is made of sufficient smalls instead of continuous infinite smalls.
My point is, most of caculus's success is built on descrete approximation.
#1377 Re: Help Me ! » a b + c d = 6 && a c - 3 b d = 5 » 2006-04-06 13:16:56
(a+d)(b+c) = 6+5+4bd
#1378 Re: Help Me ! » √ (10+2√5)=?? » 2006-04-06 13:05:29
But d ∈ N => exists k ∈ N : k^c=d.
for more illustrative
<=> ⇒ a/b=q∈N ⇒ d=q[sup]c[/sup]#1379 Re: Help Me ! » I need help BIG TIME!! » 2006-04-06 12:55:56
2/π ≈ 2/3.14 =200/314=100/157
#1380 Re: Help Me ! » a question in the DETERMINANTS » 2006-04-06 12:44:25
#1381 Re: Help Me ! » Latex » 2006-04-06 12:26:23
#1382 Re: Help Me ! » Latex » 2006-04-06 12:21:18
#1383 Re: This is Cool » The Shape of a Suspension Bridge's Main Cable » 2006-04-05 23:31:39
NOTICE the KNOTS (corrected), they are streched downward.
Franklin's guess is right, too. Even the knits doesn't form a parabola but a parabola-catenary mix.
For Post 12, you cannot get a parabola knits trajectory.
the tangent (slope) grows by 0, 2, 4, 6
height grows by 0, 2, 6, 10 =n(n+1)
length l= (n-1/2)Δx set Δx=1 n=l+1/2
n(n+1)= (l+1/2)(l+3/2) the function of right knits isn't symmetric about the axis in the graph, thus left knits have another function (l-1/2)(l-3/2)
Two parabolas
#1384 Re: Help Me ! » Latex » 2006-04-05 23:18:51
uh, i used to think the latex here is too old.
#1385 Re: Help Me ! » √ (10+2√5)=?? » 2006-04-05 23:17:25
you can simplify
as 2+√5#1386 Re: Help Me ! » √ (10+2√5)=?? » 2006-04-05 23:11:17
eazy, if a is a rational, it can be presented as N/M , where N and M are both integers.
N²/M²=a², thus a is a rational. but a is not.
to be strict 10+2√5 is rational <=>√5 is rational (proved by simple fraction algebra)
The last part is very difficult, it usually lies on a Math Analysis book's page.
Proporsition: √5 cannot be expressed as N/M, where N and M are both integers.
Proof:
suppose √5 can be expressed as N/M, thus its simpified form would be p or p/q, where p and q are both integers. it cannot be p alone, since no integer p satisfy pp=25
p²/q²=5, p²= p p =5, thus p|5 , then p²|25 and q|5 is invalid(don't know the english words)
∴when p²/q² is an integer L, L|25 but L cannot.
Hence the assumption is false.
#1387 Re: Help Me ! » Complicated integration » 2006-04-05 16:18:40
is a hyperfunction, which cannot have an explicit expression
#1388 Re: Help Me ! » Complicated integration » 2006-04-05 14:01:38
difficult, lol
#1389 Re: Help Me ! » √ (10+2√5)=?? » 2006-04-05 13:55:13
it has no solution, my software told me
#1390 Help Me ! » √ (10+2√5)=?? » 2006-04-04 18:11:33
- George,Y
- Replies: 11
Can anyone solve it explicitly out?
find positive irrantional a, who satisfies a²=10+2√5
#1391 Re: Help Me ! » Latex » 2006-04-04 18:07:46
Try this
yeah
#1392 Re: Help Me ! » a question in the DETERMINANTS » 2006-04-04 18:05:07
Reread the determinant properties, and then you will understand
|column1 column2 column3a+column3b|
=|column1 column2 column3a|+|column1 column2 column3b|
#1393 Re: Help Me ! » a question in the DETERMINANTS » 2006-04-04 02:56:56
decompenent the last colume, and reform
| X X² 1 +X³ | |1 X X² | |1 X X²|
| Y Y² 1+Y³ | = -1(- 1)| 1 Y Y² | +XYZ| 1 Y Y²| = (1+XYZ)VD
| Z Z ² 1+Z³ | |1 Z Z ²| | 1 Z Z ²|
VD -Vander monde Determinant
if x≠ y≠ z
xyz=-1
#1394 Re: This is Cool » The Shape of a Suspension Bridge's Main Cable » 2006-04-04 01:41:35
an alternative model has been developed
A lot of films have such a horrible scene:
heros dashing on a broken rope bridge, and luckily reaching the end.
The rope , similar to the cable of a suspension bridge, should break near one end, rather than in the mid point-- you may verify this.
#1395 Re: This is Cool » The Shape of a Suspension Bridge's Main Cable » 2006-04-04 01:01:18
Many thanks, mathsyperson 
#1396 Re: Help Me ! » Hi...am in need of ur help..in vector calculus.please help me. » 2006-04-03 22:15:02
How does the point move?
#1397 Re: Help Me ! » Latex » 2006-04-03 22:12:00
good luck 
#1398 Re: Help Me ! » Latex » 2006-04-03 17:33:24
\times
#1399 Re: Help Me ! » Latex » 2006-04-03 17:31:59
[ \left[ \begin{array}{ccc}
a & b & c \\
d & e & f \\
g & h & i \end{array} \right)\]
#1400 Re: This is Cool » I disagree with » 2006-04-03 17:19:37
The poor of induction
Russel once said this story
a hen saw her master giving her food one day.
she saw the same thing the 2nd day, the 3rd day...
after many many days, she concluded an ultimate truth based on induction
- he will always give me food.
the next day, she was killed by her master.
This is a philosophical attack on all human knowledge, and a underpinning concept of many films, such as Matrix.
Here i say, imagining infinity is an art, you can have whatever imaginations as you like.it's like Plato's idea. there isn't too much sense...