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#176 2013-02-11 01:05:37

Agnishom
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Re: A few questions

bobbym wrote:

Hi;

You can also get quite close using:

http://latex.codecogs.com/gif.latex?\large%20\bold{%205^{44}=%20\frac{10^{44}}{\left%20(%202^{10}%20\right%20)^4%20\cdot%202^4}}

Hi bobbym,
What should I be doing after getting this form?

Hi stefy,
How? If I could have approximated the logarithm of 5^44, then there would have been no problem at all. Can you do it?

Last edited by Agnishom (2013-02-11 01:07:04)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65

#177 2013-02-11 01:18:08

bobbym
Administrator

Online

Re: A few questions

10^44 is a 45 digit number.

2^10 ≈ 1000 = 10^3

(10^3)^4 = 10^12

10^44 / (10^12 * 2^4) = 10^32 / 2^4

Now 2^4 = 1.6 *10

10^32 / ( 1.6 * 10) = 10^31 / 1.6 ≈ 10^30.

10^30 is a 31 digit number. But this is only an approximation.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#178 2013-02-11 01:23:52

Agnishom
Super Member

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Re: A few questions

Yes, yes, I get it

Well, what had stefy been talkiing about?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65

#179 2013-02-11 01:28:35

bobbym
Administrator

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Re: A few questions

You can use Taylor's series to get log(5), but it will require a little bit of calculus.

If you want to see how...

Last edited by bobbym (2013-02-11 02:15:30)

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#180 2013-02-12 00:24:08

Agnishom
Super Member

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Re: A few questions

Indeed I want to see,

My problem is that I am not acquainted enough with calculus

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65

#181 2013-02-12 00:26:39

bobbym
Administrator

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Re: A few questions

You are a little young for your school system to have taught you it. They prefer a gradual introduction to it.

I am using log(x) to denote the common logarithm and ln(x) as the natural log.

You start with the Mclaurin series

http://latex.codecogs.com/gif.latex?\small%20\inline%20\dpi{120}%20\bg_green%20\fn_cs%20\ln\left%20(\frac{1+x}{1-x}%20\right%20)=2%20x+\frac{2%20x^3}{3}+\frac{2%20x^5}{5}+\frac{2%20x^7}{7}+...+

If we substitute x = 2 / 3 in the we get:

http://latex.codecogs.com/gif.latex?\small%20\inline%20\dpi{120}%20\bg_green%20\fn_cs%20\ln\left%20(\frac{1+\frac{2}{3}}{1-\frac{2}{3}}%20\right%20)=%20\ln(5)\approx%20\frac{2\%202}{3}+\frac{2}{3}%20\left(\frac{2}{3}\right)^3+\frac{2}{5}%20\left(\frac{2}{3}\right)^5+\frac{2}{7}%20\left(\frac{2}{3}\right)^7%20=%201.600261284211901

So ln(5) ≈ 1.600261284211901

But we needed log(5) not ln(5)! How do we get it?

We use this relationship

http://latex.codecogs.com/gif.latex?\small%20\inline%20\dpi{120}%20\bg_green%20\fn_cs%20\log(x)=\frac{\ln(x))}{\ln(10)%20}

http://latex.codecogs.com/gif.latex?\small%20\inline%20\dpi{120}%20\bg_green%20\fn_cs%20\log(5)=\frac{\ln(5))}{\ln(10)%20}

http://latex.codecogs.com/gif.latex?\small%20\inline%20\dpi{120}%20\bg_green%20\fn_cs%20\log(5)=\frac{\ln(5))}{\ln(2)%20+%20\ln(5)}

http://latex.codecogs.com/gif.latex?\small%20\inline%20\dpi{120}%20\bg_green%20\fn_cs%20\log(5)%20\approx%20\frac{1.60026}{0.693\,%20+1.60026}%20\approx%200.698970004

which is quite close to the true value.

Last edited by bobbym (2013-02-12 01:37:12)

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#182 2013-02-12 00:54:28

Agnishom
Super Member

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Re: A few questions

Let me try it out

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65

#183 2013-02-12 01:03:23

anonimnystefy
Real Member

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Re: A few questions

Hi bobbym

http://latex.codecogs.com/gif.latex?\frac{\ln{\left%20(1+\frac{2}{3}%20\right%20)}}{1-\frac{2}{3}}\neq%20\ln{5}

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#184 2013-02-12 01:07:24

bobbym
Administrator

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Re: A few questions

Please hold on the latex maker is not holding up, I am aware of that and am editing the original post.

All done!

Last edited by bobbym (2013-02-12 01:27:57)

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#185 2013-03-15 03:32:52

Agnishom
Super Member

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Re: A few questions

Please help me with the problem attached


Uploaded Images
View Image: Infinite Circles.PNG      

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65

#186 2013-03-15 04:07:38

bob bundy
Moderator

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Re: A few questions

hi Agnishom,

I'm not getting this yet.  I've drawn a line L .  Now it says 'on a straight line l' so I assumed that the circles had their centres on the line, and that each circle touches the ones on either side of it.  That covers the 'externally tangential to circle(n-1) and circle(n+1) but apparently also tangential to L itself.  How does that happen?  And I haven't even got to the second sentence yet.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#187 2013-03-15 07:05:57

anonimnystefy
Real Member

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Re: A few questions

I am getting 1/2.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#188 2013-03-15 09:42:50

bobbym
Administrator

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Re: A few questions

Hi Agnishom;

bobbym wrote:

A picture is worth a thousand words.

For people like me who are geometrically challenged this problem is a nightmare. So far I have come up with 10^16 different possible drawings that to me fit those constraints.

Now I am busy looking up externally tangent, internally tangent, tangerine tangent... in the hopes of what externally tangent to the line means. Intersects at one point?

I see that bob has got his circles with their centers on the line, I have lifted my circles and it was hard to do, after all there are an infinite amount of them, to roll on the line. That takes care of externally tangent. Now this second bunch of circles, where do they go?

John McCarthy wrote:

As the Chinese say, 1001 words is worth more than a picture.

Maybe I shouldn't need the diagram...

Last edited by bobbym (2013-03-15 18:08:18)

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#189 2013-03-15 12:59:39

Agnishom
Super Member

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Re: A few questions

Bob, if you want I can give a diagram

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65

#190 2013-03-15 13:12:12

Agnishom
Super Member

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Re: A few questions

This is the only diagram I can imagine.

A rough sketch though...

1001 Words ≈ 7 KB
1 picture > 100 KB

Obviously, a picture is worth more....


Uploaded Images
View Image: Infinite Circles.PNG      

Last edited by Agnishom (2013-03-15 13:14:14)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65

#191 2013-03-15 13:45:43

Nehushtan
Power Member

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Re: A few questions

Agnishom wrote:

Please help me with the problem attached

This is what I got.


Let
be the centre of
and
the point of contact of
with
. Let
be the centre of
and
the point of contact of
with
.

Let
be the point on
such that
is a rectangle. Applying Pythagoras’s theorem to
gives
.

Let
be the point on
such that
is a rectangle. Applying Pythagoras’s theorem to
gives
.

Let
be the point on
such that
is a rectangle. Applying Pythagoras’s theorem to
gives
.

Then














Hence:

Last edited by Nehushtan (2013-03-15 13:53:34)

Holding on to anger is like drinking poison and expecting the other person to die.

#192 2013-03-15 17:19:41

bobbym
Administrator

Online

Re: A few questions

Hi Agnishom;

Thanks for the drawing.

Last edited by bobbym (2013-03-15 20:19:25)

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#193 2013-03-15 18:18:18

Agnishom
Super Member

Offline

Re: A few questions

Thanks Nehushtan
I shall ask you if I have any doubts

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65

#194 2013-03-16 12:54:42

Agnishom
Super Member

Offline

Re: A few questions

Please upload a diagram, I really do not understand from "Applying Pythagoras Theorem..."

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65

#195 2013-03-17 03:09:30

Nehushtan
Power Member

Offline

Re: A few questions

Here you go.


Uploaded Images
View Image: Circles.png      

Holding on to anger is like drinking poison and expecting the other person to die.

#196 2013-03-17 15:06:15

Agnishom
Super Member

Offline

Re: A few questions

Thank you smile

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65

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