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

You are not logged in.

- Topics: Active | Unanswered

We want to calculate the value of x if x were this continued fraction:

On our way, we will see how quadratic equations are involved.

*Last edited by Agnishom (2014-10-26 23:50:11)*

'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.

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,126

Responding To Thread As Being Told.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

What is amazing is that the whole fraction in the large box and the part inside the smaller box is just the exact same since both constitute the same iterations infinite times.

Do you agree?

'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.

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,126

I don't understand.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

Do you think that the whole continued fraction and the part inside the smaller box is just the same?

'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.

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,126

Yes

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

Great!

On the basis of that, we can write it as this:

Can we?

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

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

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,126

Yes

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

Do you know how to solve this?

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

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

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,126

x^2 = 1 + x

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

Great!

Use the quadratic formula from there onwards

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

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

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,126

For?

Lets learn more.

*Last edited by David (2014-10-27 00:40:32)*

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

Do we know what the quadratic formula is?

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

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

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,126

Explain

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

It is a shorthand formula that can solve *any* quadratic equation just by plugging values without the need of any intelligent thought!

*Last edited by Agnishom (2014-10-27 01:17:34)*

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

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

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,126

ax^2 + bx + c = 0

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

Okay let me write down the formula here!

What is the value of a,b and c in this equation: x^2 +5x+6 =0?

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

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

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,126

I haven't learnt that.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

You will now.

Do you agree that every quadratic equation is reducable to the form in post 16?

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

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

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,126

I don't think so?

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

Well, it is.

Is x^2+5x+6 of that form?

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

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

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,126

Yes.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

What are the values of a, b, and c?

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

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

Offline

**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,126

a = ^2 b = 5 c = 6

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

No, a=1. Do you agree?

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

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

Offline