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I'm done with the painting and the surprise I got was that I realised that I do not paint so well like my classmates.

Ancient Indian Mythology is nice. This One is not so ancient, it is only around 500-600 years old.

My favorite goddess philosophy is Devi Shukta or the Chandi.

'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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Hi;

Painting is an art.

My favorite goddess philosophy is Devi Shukta or the Chandi

I do not know that one.

**In mathematics, you don't understand things. You just get used to them.**

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I think it is better known as Devi Mahatmya

It is the main philosophy behind Goddess Durga or Kali.

It contains three episodes where:

1. From the ears of Vishnu, two demons Madhu and Kaitabha emerge. Vishnu tried so much but could not kill them. Under the goddess's influence at last, they become full of ego and then they were killed by Vishnu at last.

2. The Demon Mahisasura was killed.

3. The demons Sumbha and Nisumbha were killed. In this episode the goddess reveals that she alone is real and thus she absorbs the evils into herself

This have been interpreted by philosophers to have great inner meanings.

The main concept of the first episode is the establishment of the truth. The second symbolises the *Pran Pratistha*(The establishment of life). while the third symbolises *Ananda Pratistha*(The establishment of eternal joy).

When a soul goes through all these stages he is outside the Reincarnation cycle and enjoys freedom from all kinds of bondage.

'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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Hi;

Thanks, I did read about her before.

**In mathematics, you don't understand things. You just get used to them.**

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From barbie1902?

I think I would celebrate the occassion by reading the Devi Mahatmya Theory book rather than doing what normal people do.

'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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

I doubt it. Probably read about it on my own.

That is good.

**In mathematics, you don't understand things. You just get used to them.**

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Ok, what should I be computing?

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Compute say 100 terms of that series and tell me what you get.

**In mathematics, you don't understand things. You just get used to them.**

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3.1315929035585537

It cconverges very slow

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Yes, although there is a big = sign there the series is useless for computation. We would need many millions of terms for 5 or 6 digits of accuracy.

So, we can accelerate the series. Not too hard but leading us away from the point. Or, we can use another series. At last count there are about 160 of them.

**In mathematics, you don't understand things. You just get used to them.**

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Wow. That is pretty impressive.

I tried the AM-GM inequality around a year ago. It works well.

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Want to see the one I developed?

**In mathematics, you don't understand things. You just get used to them.**

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Surely, I do!

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Okay, let me find it.

Sorry, mine is gone and I do not remember how to derive it so let's use Machin's formula instaed.

**In mathematics, you don't understand things. You just get used to them.**

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?

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Yes, believe it or not that converges to pi and was one of the earliest used to get lots of digits.

**In mathematics, you don't understand things. You just get used to them.**

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But that does not look like any infinite series. How can you use the term 'converge'?

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Do you remember the Taylor series for arctan(x)?

**In mathematics, you don't understand things. You just get used to them.**

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So, thats the same thing written in a different way?

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Yes, but we have two series to sum instead of one.

With n = 10 we get

3.1415926535897932947 which has 17 correct digits!

**In mathematics, you don't understand things. You just get used to them.**

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```
>>> 16*atan(1.0/5.0) - 4 *atan(1.0/239.0)
3.1415926535897936
```

I am supposed to get 3.1415926535897932

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

You were probably a victim of subtractive cancellation. We have not covered that yet. We are back in the world of computation and much mathematics does not hold or has to be modified.

For right now:

Please try post #45 and compute those series.

**In mathematics, you don't understand things. You just get used to them.**

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That is what has been done in post 46. Don't you think?

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

In post #46 you plugged in to a formula. Unfortunately in computation summing the series and plugging in are two very different algorithms. In math you of course expect the same answer. In computation you do not!

Also, when you plug in it is a black box. You do not see what method the program used to evaluate those trig functions. When you sum the series you know exactly what was used.

Remember, Machin, Gauss and Dase did not plug in and neither do the guys who get billions of digits.

I am going to eat, see you later.

**In mathematics, you don't understand things. You just get used to them.**

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ok, I will do it

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

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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