Georgia School Board Bans 'Theory of Math'

[Colonel Olrik]

How do they get the calculations for pi, anyway? It can't be represented with a fraction, and you can't know the exact circumfernce and diameter of a circle without knowing pi, unless you have really precise measuring equipment.

There are many analytical methods for computing pi.

For example, using Taylor's formula for arctan(x), we eventually get to the relationship discovered by John Machin:

pi = 16* arctan(1/5) - 4 * arctan(1/239) [warning, in radians!]

I suspect this was more than you wanted to know, but

[Durandal]

That formula is a bit redundant, since it uses radians, which are based on a known value of pi. It would be like me integrating a circle by changing to polar coordinates to derive by by dividing the resultant area by r^2.
You could derive pi by doing a limit-notation integral on a circle, but that would be extraordinarily tedious.

[Darth Yoshi]

That reminds me. Can anyone mathematically prove that 1+1 actually does equal 2? I've never been able to do it.

[Faram]

"Proof" that 1 + 1 = 1

a = 1
b = 1

a = b
a2 = b2
a2 - b2 = 0
(a-b)(a+b) = 0
(a-b)(a+b)/(a-b) = 0/(a-b)
1(a+b) = 0
(a+b) = 0
1 + 1 = 0
2 = 0
1 = 0
1 + 1 = 1

This is complete BS but where do it screw up?

Woops forgot da Link

[Colonel Olrik]

"Proof" that 1 + 1 = 1

a = 1
b = 1

a = b
a2 = b2
a2 - b2 = 0
(a-b)(a+b) = 0
(a-b)(a+b)/(a-b) = 0/(a-b)
1(a+b) = 0
(a+b) = 0
1 + 1 = 0
2 = 0
1 = 0
1 + 1 = 1

This is complete BS but where do it screw up?

SPOILER







fifth line, divide by zero

[Faram]

That reminds me. Can anyone mathematically prove that 1+1 actually does equal 2? I've never been able to do it.

Found this:

Date: 28 Feb 1995 23:35:47 -0500
From: Dr. Ken
Subject: Re: WHY does 1+1=2? Nobody that I ask has been able to answer that

Here's a good reason that nobody you ask has been able to tell you
WHY 1+1=2. I quote from the February edition of the Newsletter of
the Mathematical Association of America:

...when was the last time you saw a proof of a real theorem that
followed the strict rules of logic? Remember, it took Whitehead
and Russell 362 pages of formal deduction in their mammoth work
_Principia_Mathematica_ before they were able to prove 1+1=2.

It was nice that I happened to notice this yesterday, just in time for
your question. _Principia Mathematica_ was a work that attempted
to codify all of the existing mathematics at that time, in an absolutely
rigorous fashion. After all, there are almost no proofs these days that
follow the strict rules of logic; they are simply chains of reasoning
that convince mathematicians that such a formalized proof _could_ be
given, but nobody actually wants to see them.

But you are wise to ask why 1+1=2. I suggest you check out Whitehead
and Russell's book, and see what they have to offer.

-Ken "Dr." Math

Here

Better start reading

[Durandal]

1 + 1 = 2 because that's the way we've defined the number line.

[Colonel Olrik]

1 + 1 = 2 because that's the way we've defined the number line.

MY GOD!! 362 pages worth of demonstration reduced to a single line!

The man is a GENIUS!!

*gives Durandal a BIG cookie*

[Durandal]

I dunno ... seemed pretty obvious to me...

:)

[SWPIGWANG]

gah again :/

Anyway, lets just say stupid dozen axioms....

[NecronLord]

Speaking of pi, what's the point of calcuating it to 5 billion digits? Just 3.14 will get you through college, or at least in America.

The only thing funnier than someone going against evidence is when they use the Bible as proof.

It will?

Hell to get though first year in secondary school (age 10) I had to learn 3.14159
Or did I just have sadistic maths techers?

Code: Select all

one plus one = Two

Take one penny (or cent)

Lay another down next to it

Count them.

[Slartibartfast]

Speaking of pi, what's the point of calcuating it to 5 billion digits? Just 3.14 will get you through college, or at least in America.

The only thing funnier than someone going against evidence is when they use the Bible as proof.

It will?

Hell to get though first year in secondary school (age 10) I had to learn 3.14159
Or did I just have sadistic maths techers?

You could get by just by knowing that pi=3.142 should be enough in most courses. Usually Physics and other applied math might let you squeeze with 3.14, while pure math courses will require you at least 4 digits (3.1416)

[Colonel Olrik]

Bah. I have a TI89 calculator. It has faithfully served me troughout college. Thanks to her, I always know that pi = 3.1415926535898

[Asst. Asst. Lt. Cmdr. Smi]

I've memorized 3.14159265358979323 out of a book. I'm not bothering to go any further.

[Nick]

1 + 1 = 2 because that's the way we've defined the number line.

MY GOD!! 362 pages worth of demonstration reduced to a single line!

The man is a GENIUS!!

*gives Durandal a BIG cookie*

Here's some free advice - don't study pure math. If you do, you may be inclined to expand on Durandal's perfectly accurate explanation above, as I do below (this is probably somewhat incorrect - I'm doing it from memory, and I studied it in one subject about 5 years ago).

CAUTION: This doesn't actually add anything much to Durandal's explanation - but it is an interesting exercise in pure math. How are the basic mathematical operations defined formally by mathematicians?

1. We accept that set theory works (this is actually three axioms, but I ain't describing them here - mainly because I can't remember them).
2. We accept the existence of a 'base value' that I will call '0'
3. We accept the existence of a 'succesor function', which I will write 'inc(x)'

Successive application of the succesor fucntion gives us an infinite chain of numbers, which we will call the natural numbers (N).

Now, we define a relationship within the natural numbers, such that the relationship has the properties:
Reflexive:
for all A in N, A is related to A
Commutative:
for all A,B in N, if A is related to B, then B is related to A
Transitive:
for all A,B,C in N, if A is related to B, and B is related to C, then A is related to C

We will call this relationship equality, and write "A is related to B" as 'A = B' (interestingly, any relation, for any set, with the above properties is called an 'equivalance relation')

Next we define a more complex relationship. This time, it is defining pairs of natural numbers in relation to their equivalence to single natural numbers:
Zero-identity:
for all A in N, (A,0) is equivalent to A
Succesor relation:
for all A in N, (A,inc(0)) is equivalent to inc(A)
Commutative inputs:
for all A,B,C in N, if (A,B) is equivalent to C, then (B,A) is equivalent to C

We will call this addition, and write the input pairs such as (A,B) as "A + B", giving us familiar expressions of the form 'A + B = C'

So, how do we go about getting "1 + 1 = 2"?

Well, we write it as 'inc(0) + inc(0) = inc(inc(0))'

Which fits the definition of the succesor relation part of addition.

So why is "1 + 1 = 3'" wrong? Because it doesn't fit the definition of addition.

[Nick]

CAUTION: This doesn't actually add anything much to Durandal's explanation - but it is an interesting exercise in pure math. How are the basic mathematical operations defined formally by mathematicians?

And you'll notice that even my definition assumes a lot (the axioms of set theory for a start).

I can believe many, many pages would be required for an actual mathematical proof (as opposed to a 'lets hit some of the high points' like the one our lecturer showed us. . .)

[Nick]

EDIT: Make that a triple post

[Nick]

EDIT: Ah, the double-post rears its ugly head.

[Zoink]

You could get by just by knowing that pi=3.142 should be enough in most courses. Usually Physics and other applied math might let you squeeze with 3.14, while pure math courses will require you at least 4 digits (3.1416)

It all depends on the number of significant figures you need. In university, the applied math courses wanted answers, so we used a calculator; for pure math courses that wanted equations, the equations were solved with the symbol *pi* in it. While I have it memorized to 3.14159265358979324... the last time I actually had to muliply pi w/o a calculator was in high school, and we used 3.14.