Math Is Fun Forum

Anyone any idea with Microsoft's Encycropedia? (if miss-spelled, sorry)

Thank you Ricky! I will try them.

4

Thus exponetial term cancelled out

b)

No, it has nothing to do with regression-it has only something to do with geometry and calculus. Trust me.

Hey guys!

Why don't we make it simpler? After all the auther said "guessing" instead of exact number.

If the ball placement can be monotonous when in a large amount, we can calculate the limit of the ratio of occupying space and waste space when the amount goes to "infinity", thus we can give an approximate answer.

I can start with the 2-D case-Circles instead of Balls
Like this pattern:
.....................
...OOOOOOO...
...OOOOOOO...
...OOOOOOO...
......................
Focus at one black circle in the center and its surrounding 6 balls, (in fact all touching) and we can find a sexangle outbound it as its ideal area in the whole  area consumed by balls. Think of a bee-nest's side, and imagine you can place circles in to each cell, and that if your each circle is big enough to tough 6 sides of the cell, they are in the space-economy allignment. You cannot make the circle consume lesser space.

O  O
O ● O
  O O

And the circles area percentage of the whole is just the ratio of area of each circle to that of the cell.

            Pi*r*r
___________________ = 90.7%
       
  6*(1/2*r*(rSec60°))

And if you know the whole area, guage the circled area using the percentage, and divided by each circle's area, you may find an approximate answer for their amount.

How about 3-D case? The ball case? I don't know.

Hello guys, I am now in Waltham, a place near Boston, persuing my expensive but good  Master's of degree in Finance as an international student.

My school does teach a lot of maths, but they don't tell the whole thing, they just tell how to do this, how to do that, what is this, what is that thing because I am in a Finance Grad Program rather than anything else.

My course work is thus simple in a way, but boring in another perspective. -Hope you have great fun "wasting" your time in adventuring maths when you are still so young at undergraduate or below that, without urgent need for career preparation.

BTW: Does anyone know whether there is a good physics-maths journal or logic-maths journal in the Greater Boston Area? Many thanks in advance.

Can you write out v[sub]t[/sub] explicitly, luca? There might be other ways than computing if you can do so.

Tks!

But well, it's a little bit hard to add those equipments on a tiny thin slide rule. For example, you can use a flexible electric resistant to record the position where the hairline is in. But it will be a larger device to tell how large the resistant is
+
|The starting position
|_______________________________ 
                                  |The hairline
                                  -
By dectecting the current magnitude from + to - under a certain voltage, we can determine how far the hairline is from the starting postion, then we have to transform the distance to real exponetial scales on the slide rule.

Perhaps there is a simplier way out of it. Is there a natural law that naturally changes exponetially? Then we may not employ the linear current-resistant phenomenon.

"but in calculus you are given all sorts of random graphs from all over the place and you're supposed to differentiate or integrate them without even knowing what they are?"

--No, under such circumstances it is only possible to make numerical approximations. By computer, of course.

"I want you to like this."
"I don't want you to dislike this."

In logic, the negative of "like" is not exactly "dislike", because surely there are other options like neutral.

So how about this pair?
"I think you like this."
"I don't think you don't like this."

Okay, let's see

B_____A_______C

B is 5 metres left of A.

B=A-5

And C is 7 metres right of A.
C=A+7

How long is C right of B?
The answer should be:
C-B=A+7-(A-5)
The answer, as you can varify, is 12.
Ah-ha!
How do you calculate --5?  = +5.

Why?

Because left is negative/reverse for right, and left-end is negative in the formula of d=C-B  then the two negative effect cancells each other out. (you can go to the explaination now)

Or another model.
A, B, C = 3 persons. right= higher, left= shorter.
Now do it again. You will find that the shorter the shortest person than the middle person, the taller the tallest one than the shortest.

When comparison appears, you have this interesting cancelling out effect, which may be the origins of negative negative= positive.

BTW: The Explaination
If I say A is 5 metres right of B, and C is 7 metres right of A, you probably will tell that C is 12metres right of B without any hesitation.

But now we have only B 5 metres left of A.
First, left is reverse to right. So B is -5 metres "right" of A, as we can define. "-" here only means the reverse.
Now, if one thing is right of another, the other is just left of this one thing with the same distance.
So when you swap A and B in the sentence B is x metres right/left of A, you get a reverse between left and right.
As mentioned before, left itself is the reverse/negative of right, and now you reverse left, then you definately have:
Right___Left___Right:
Reverse then reverse comes back. Or reverse the reverse gets it back.

Thus A is 5 metres right of B.
we can abstract this "Reverse then reverse comes back" effect to a simple expression
--=+ or --x=x
as in the case -(-5)=5, which also stands in a bit more complex situation 7-(-5)=12