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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

Yes, but what has that have to do with pizza?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Nothing. We are making gel candles for school project. Why is a gel candle considered a good gift?

'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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

Because the people who sell the materials say so.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Why is it not?

'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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

What makes anything a good gift?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 563

That pizza sounds good:)

Have you covered the least squares - orthogonality property of these approximations?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

Hi EVW;

Not yet on both!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 563

That post earlier about .999999... it does sound like that guy you told me about:(

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

Read the other ones, have you?

These fits are both least square and orthogonal. This makes them very desirable. Along with the periodicity property.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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bobbym wrote:

What makes anything a good gift?

I've no idea

'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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

Do you agree with her that is GiB over there?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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bobbym wrote:

Do you agree with her that is GiB over there?

Sounds like good news but when did ElianaVW tell that?

*Last edited by Agnishom (2014-02-20 16:10:46)*

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

Post #33.

I have to go eat now, we will continue later. Have a good day at school.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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That is not likely to be GiB He does quality posts.

By the way, today is the last day of my secondary schooling

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

I never saw him ever do a quality post.

Let's do the fourier series for x^2.

```
f[x_] := x^2;
a0 = 1/(2*\[Pi]) Integrate[f[x], {x, -\[Pi], \[Pi]}];
a[n_] := 1/\[Pi] Integrate[f[x] Cos[n*x], {x, -\[Pi], \[Pi]}];
b[n_] := 1/\[Pi] Integrate[f[x] Sin[n*x], {x, -\[Pi], \[Pi]}];
```

All the b's are zero and

`a0 + a[1] Cos[x] + a[2] Cos[2 x] + a[3] Cos[3 x] + a[4] Cos[4 x]`

yields:

`Plot[{x^2, \[Pi]^2/3 - 4 Cos[x] + Cos[2 x] - 4/9 Cos[3 x] + 1/4 Cos[4 x]}, {x, -\[Pi], \[Pi]}]`

quite a good fit as you can see below.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Thanks, I tried that. Do you have an exercise for me?

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

Did you get the same answer?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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I just copy pasted what ever you wrote. What answer?

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

Okay, you are ready to stand on your own two feet.

Please get the Fourier series of

[I made a small edit to the problem.]

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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```
In[61]:= a[0] + a[1] Cos[x] + a[2] Cos[2 x] + a[3] Cos[3 x] +
a[4] Cos[4 x] + a[5] Cos[5 x] + a[6] Cos[6 x] + a[7] Cos[7 x] +
b[0] + b[1] Sin[x] + b[2] Sin[2 x] + b[3] Sin[3 x] + b[4] Sin[4 x] +
b[5] Sin[5 x] + b[6] Sin[6 x] + b[7] Sin[7 x]
Out[61]= 2/\[Pi] - (2 Cos[2 x])/(3 \[Pi]) - (2 Cos[4 x])/(
15 \[Pi]) - (2 Cos[6 x])/(35 \[Pi]) + Sin[x]/2
```

It is not really a good fit still

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

Please post a picture of the fit.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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I'll but now it'll be done by GNU Plot rather than M because now I am running Linux

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

Okay, lets see the plot of both functions superimposed on each other.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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I am getting this error in my CAS

```
ontext: too many contexts.
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plot2d: expression evaluates to non-numeric value somewhere in plotting range.
```

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

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,357

Take a look at mine in the blue and yours in the black. What do you notice?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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