Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,942

I am here and waiting.

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

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

```
>>> def pi(n):
s = Decimal()
for i in xrange(0,n+1):
s += ((-1**i)*((Decimal(1)/Decimal(5))**(2*i+1)))/((2*i)+1)
s *= 16
for i in xrange(0,n+1):
s -= 4*(((-1**i)*((Decimal(1)/Decimal(239))**(2*i+1)))/((2*i)+1))
print s
>>> pi(10)
-3.226984365524281777452846574
```

What is wrong?

'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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,942

Hi;

```
>>> def pi(n):
s = Decimal()
for i in xrange(0,n+1):
s += ((-1**i)*((Decimal(1)/Decimal(5))**(2*i+1)))/((2*i)+1)
s *= 16
```

Please run that and post the answer. Then run the second piece and post that answer.

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

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

```
>>> def pi(n):
s = Decimal()
for i in xrange(0,n+1):
s += ((-1**i)*((Decimal(1)/Decimal(5))**(2*i+1)))/((2*i)+1)
s *= 16
print s
>>> pi(10)
-3.243720864865314995238473720
```

'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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,942

Put a parentheses around that -1.

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

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

```
>>> def pi(n):
s = Decimal()
for i in xrange(0,n+1):
s += (((-1)**i)*((Decimal(1)/Decimal(5))**(2*i+1)))/((2*i)+1)
s *= 16
for i in xrange(0,n+1):
s -= 4*((((-1)**i)*((Decimal(1)/Decimal(239))**(2*i+1)))/((2*i)+1))
print s
>>> pi(10)
3.141592653589793294747374859
>>> pi(100)
3.141592653589793238462643384
```

I'm so stupid.

My apologies for being late to reply. I had been dining.

'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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,942

Hi;

π = 3.14159265358979323846264338328...

So you see you have lots of digits from only 100 iterations.

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

Offline

Yup

'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

Offline

```
>>> getcontext().prec = 100
>>> pi(100)
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117064
>>> pi(10000)
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117064
```

So, already a lot

'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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,942

That particular formula was used when Shanks calculated pi to 707 places without an electronic computer. He used a human one. But there was a mistake on the 527 digits so all the rest from there on are wrong. Still, it was a record that lasted until modern times and electronic computers.

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

Offline

Did he use himself?

'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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,942

A guy called Dase was used. He was an idiot savant capable of multiplying two 100 digit numbers in his head in 5 or 6 hours. He did all the computation.

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

Offline

isn't 5 or 6 hours a lot?

'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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,942

Yes, but it is a mistake. Shanks did the calculation in 1873 and Dase was dead by 1861 so he must have used someone else that was similar. Also, it took Dase 8 hours to multiply two 100 digit numbers.

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

Offline

How were such guys found/developed?

'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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,942

[deleted by administrator]

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

Offline

Do we really need that ability?

'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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,942

[administrative delete]

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

Offline

Why should they try to hide it? Who are they, by the 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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,942

The same that we discussed in the PM, among others.

[administrative delete]

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

Offline

Who are special then?

Those people are power greedy ones. What can happen to them if people compute faster?

Just because someone is able to compute very fast, that does not mean that he is very wise. Mere computation won't take mathematics farther.

'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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,942

Computation is a very important part of math. A point I have been trying to make since I got here. It represents a new way of thinking about things.

Mere computation won't take mathematics farther.

That is the end result of what I have been saying. Nothing could be further from the truth.

But it is only the tip of the iceberg when we talk about the hidden capabilities of a human being.

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

Offline

Which people are special then?

Why did you have to delete those comm?ents?

'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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,942

They are about things that I do not wish the entire internet to see.

Special is the wrong word. Let's just say those are common abilities.

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

Offline

Yes, but what is special, then?

'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

Offline