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: 84,516

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

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

Offline

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'

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,516

Because the people who sell the materials say so.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

Offline

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'

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,516

What makes anything a good gift?

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

Offline

**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 288

That pizza sounds good:)

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,516

Hi EVW;

Not yet on both!

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 288

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,516

Read the other ones, have you?

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

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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'

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,516

Do you agree with her that is GiB over there?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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'

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,516

Post #33.

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

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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'

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,516

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.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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'

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,516

Did you get the same answer?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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'

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,516

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.]

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

```
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'

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,516

Please post a picture of the fit.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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'

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,516

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

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

I am getting this error in my CAS

```
ontext: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
context: too many contexts.
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'

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

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,516

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

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline