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bobbym wrote:

Hi;

You can also get quite close using:

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 (2013-02-10 02:07:04)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,570

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 (2013-02-10 03:15:30)*

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,570

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

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

So ln(5) ≈ 1.600261284211901

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

We use this relationship

which is quite close to the true value.

*Last edited by bobbym (2013-02-11 02:37:12)*

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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Let me try it out

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi bobbym

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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 (2013-02-11 02:27:57)*

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Please help me with the problem attached

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,390

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I am getting 1/2.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,570

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 (2013-03-14 19:08:18)*

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Bob, if you want I can give a diagram

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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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....

*Last edited by Agnishom (2013-03-14 14:14:14)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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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 Pythagorass theorem to gives .Let

be the point on such that is a rectangle. Applying Pythagorass theorem to gives .Let

be the point on such that is a rectangle. Applying Pythagorass theorem to gives .Then

Hence:

[align=center]

[/align]*Last edited by Nehushtan (2013-03-14 14:53:34)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,570

Hi Agnishom;

Thanks for the drawing.

*Last edited by bobbym (2013-03-14 21:19:25)*

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Thanks Nehushtan

I shall ask you if I have any doubts

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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Thank you

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

**Online**