Take A Break Fellas! ... For Math Enthusiasts!

[Harmonica]

We are not yet at Level 10, but I am posting it early to give enthusiasts enough time to ponder, extrapolate and "figure" this one out. There are no tricks in this question.

If nobody gets it, then that's that. I will not be posting the answer. It would deflate & detract from the power of this "stunner" as an examination " bypass-all-24-questions-but-if-you-attempt-and-get-#25-correct, you-score 100% on-the-exam" type of power! Just sheer poetry to me!

Degree of difficulty 4+ .... out of a maximum of 4

Level 10:

Without the use of logarithmic and/or trignometric tables, sliderules, calculators, computers etc., and starting from first principles, prove the following:

cot 7½° = √2 + √3 + √4 + √6

[wilson steer]

Hey, it's not April 1st. As anyone with a mathematical background knows,

cotangent proofs are only possible by use of the highly controversial: Iwasaw decomposition formalism.

I doubt that there are any T.V. forum readers who fully understand this branch of mathematics.

I am, waiting.....

Wilson Steer.

[Kan Win]

Level 13

I interview a person for an accounting position with us and ask only one question.

What is one and one, and the person answered :- ???????????????

So what did the person answer????

Edited April 6, 2005 by Kan Win

[ProfessorFart]

6

[wilson steer]

Is 1 a prime number?

Any positive integer has a unique factorisation into primes.

1 is not a prime number, it is unique: it is a 'unit' therefore it has 'reciprocals'

1 is not a number: It is a unit.

Wilson Steer.

[TizMe]

cotangent proofs are only possible by use of the highly controversial:  Iwasaw decomposition formalism.

I think that you mean iwasawa decomposition formalism.

[Harmonica]

Hey, it's not April 1st. As anyone with a mathematical background knows,

cotangent proofs are only possible by use of the highly controversial:  Iwasaw decomposition formalism.

I doubt that there are any T.V. forum readers who fully understand this branch of mathematics.

I am, waiting.....

Wilson Steer.

there is "history" behind this question. Starting from first principles is just exactly that -- rock bottom basics in Trigonometry & Geometry & then proceeding into Algebra -- there is unquestionably quite a bit of dealing with square roots in the denominator etc.; but the beauty comes in due to the various approaches to the solution.

Even great men were born little children!

So start from "basics" and build the great man!

[Neeranam]

I studied pure mathematics at Napier University, where John Napier, inventor of logarithms went, and this stuff is above me. OK I did fail it, but I am sure other members are totally confused.

What's it got to do with Thailand anyway??

[Phil Clark]

   

Level 13

I interview a person for an accounting position with us and ask only one question.

What is one and one, and the person answered :- ???????????????

So what did the person answer????        

<{POST_SNAPBACK}>

"Are you buying or selling?"

[Harmonica]

I studied pure mathematics at Napier University, where John Napier, inventor of logarithms went, and this stuff is above me. OK I did fail it, but I am sure other members are totally confused.

What's it got to do with Thailand anyway??

Its got plenty to do with Thighland!

I showed it to 2 upper level Uni students about a year ago and they both said,

"Jha baa!"

[paulfr]

One would need to begin with Piano's Axioms to prove this formally I would think.

But for those interested in the data .....

sqrt 2 = 1.4142135623730950488016887242097

sqrt 3 = 1.7320508075688772935274463415059

sqrt 4 = 2

sqrt 6 = 2.4494897427831780981972840747059

sum = 7.5957497427831780981972840747059

-----------

sin 7.5 deg = 0.13052619222005159154840622789549

cos 7.5 deg = 0.99144486137381041114455752692856

cot = cos/sin = 7.5957542313921826723050753262621

accuracy only to about 5 decimal places

Cheers ....

[Kerryd]

   

Level 13

I interview a person for an accounting position with us and ask only one question.

What is one and one, and the person answered :- ???????????????

So what did the person answer????        

<{POST_SNAPBACK}>

The answer to this one would be eleven (1 AND 1 = 11)

I remember an article a few years back. The University of British Columbia (UBC, Vancouver, Canada), published the findings of a study in which they determined that 1 and 1 equaled 11, 2 and 2 equaled 22 and so on.

Back then, I thought it was a complete waste of time, that university students had nothing better to do than figure out something as banal as that ? Who ever the clever monkey was that made up that thesis probably got awarded a degree in mathematics for that.

[paulfr]

On second thought ....

The thesis cannot be proven because it is not true.

The two sides of the equation are NOT EXACTLY equal.

It is only an approximation.

The equal sign should have a tilde over it to indicate approximately.

~

=

Cheers ...

[Neeranam]

On second thought ....

The thesis cannot be proven because it is not true.

The two sides of the equation are NOT EXACTLY equal.

It is only an approximation.

The equal sign should have a tilde over it to indicate approximately.

I disagree, the two sides of the equation could be equal.

You are taking an approximation when you write the suare root in decimal form.

[Harmonica]

One would need to begin with Piano's Axioms to prove this formally I would think.

But for those interested in the data .....

sqrt 2 = 1.4142135623730950488016887242097

sqrt 3 = 1.7320508075688772935274463415059

sqrt 4 = 2

sqrt 6 = 2.4494897427831780981972840747059

sum = 7.5957497427831780981972840747059

-----------

sin 7.5 deg = 0.13052619222005159154840622789549

cos 7.5 deg = 0.99144486137381041114455752692856

cot = cos/sin = 7.5957542313921826723050753262621

accuracy only to about 5 decimal places

Cheers ....

Anybody who even shows up to tackle this problem gets an automatic 15% bonus. Why? Because there is room for considerable generosity while grading the answers simply because the question is tough.

Paul gets an additional 10% for initiating a bid.

But ........

this would be the logical way to go if it were possible to remember the values above, even if one did not need to look at log/trig tables -- and let us for a moment assume that there are or could be a small %age of players who would remember such detail ....

to them I would point out your 2nd last line, "accuracy only to about 5 decimal places"

Accuracy "poy-fect" is the ticket, amigo!

Good attempt, nevertheless!

Carry on!

[Harmonica]

On second thought ....

The thesis cannot be proven because it is not true.

The two sides of the equation are NOT EXACTLY equal.

It is only an approximation.

The equal sign should have a tilde over it to indicate approximately.

I disagree, the two sides of the equation could be equal.

You are taking an approximation when you write the suare root in decimal form.

Give this gentleman (Neeranam) a cigar and a 10% bonus for his accurate statement:

"You are taking an approximation when you write the suare root in decimal form."

[Darknight]

Think i like BG topics better

You guy's have to much time on your hands.

[Thetyim]

Please Sir, permission to post pictures of naked ladies to make this thread more interesting .

[phuketsiam]

permission granted

[Darknight]

Only Square root pictures allowed in this thread

[Harmonica]

Only Square root pictures allowed in this thread

[Phil Clark]

Only Square root pictures allowed in this thread

<{POST_SNAPBACK}>

<{POST_SNAPBACK}>

Harmonica,

I suspect you have had your organ in your hand (or mouth :D ) for too long to make any comment about 'roots'.

Are you unware that 'Mathsturbation' is considered 'Economic Terrorism' in the Kingdom as it deprives certain segments of society a living?

Go figure...

[Neeranam]

I think that I may possibly manage to prove it using 3 different triangle, all right handed ones, but I can't be arsed

[Harmonica]

I think that I may possibly manage to prove it using 3 different triangle, all right handed ones, but I can't be arsed

You're on the right track Neeranam. Triangles -- that's the way to go.

[Harmonica]

Only Square root pictures allowed in this thread

Harmonica,

I suspect you have had your organ in your hand (or mouth :D ) for too long to make any comment about 'roots'.

Are you unware that 'Mathsturbation' is considered 'Economic Terrorism' in the Kingdom as it deprives certain segments of society a living?

Go figure...

Say what?

[Neeranam]

I am surprised than I remember cotangent 30 degrees is √3. I learned that stuff, never used since, nearly 20 years ago.

Interesting that 7.5 is 1/4 of 30!

Remember the 1, √2 , √3 , 1 ,2 , √3 etc

Doesn't take much to prove it with this info.

[Eman]

We are not yet at Level 10, but I am posting it early to give enthusiasts enough time to ponder, extrapolate and "figure" this one out. There are no tricks in this question. 

If nobody gets it, then that's that.  I will not be posting the answer.  It would deflate & detract from the power of this "stunner" as an examination " bypass-all-24-questions-but-if-you-attempt-and-get-#25-correct, you-score 100% on-the-exam"  type of power!  Just sheer poetry to me! 

Degree of difficulty 4+ .... out of a maximum of  4       

Level 10:

Without the use of logarithmic and/or trignometric tables, sliderules, calculators, computers etc., and starting from first principles, prove the following:

cot 7½°  =  √2 + √3 + √4 + √6

<{POST_SNAPBACK}>

Take 4 angles w, x, y, z

Such that w + x + y + z = 7.5 deg

And cot(w) = √2

cot(x) = √3

cot(y) = √4

cot(z) = √6

I will show how to do this for w. Interested readers can do x, y, z

Hard to draw here, but imagine, the triangle below is inscribed in a unit circle with angle w at the center of the circle

/|

/ |

/ |

c / | a

/ |

/ |

/w _____|

b

We want the angle w, whose cotangent is √2

b

cot(w) = ---

a

b

--- = √2

a

b = a √2

We know from Pythagoras that c2 = a2 + b2 (c squared = a squared + b squared)

c2 = a2 + b2

substututing in b = a√2 from above, we get

c2 = a2 + (a√2)squared

= a2 + 2a squared

= 3a squared

But because the triangle is inscribed in a unit circle, we know c = 1, so

1 = 3a squared

1

--- = a2

3

1

--- = a

√3

And we know that b = a√2, so

1

b = --- √2

√3

√2

= ----

√3

I think this works.....

[Eman]

We are not yet at Level 10, but I am posting it early to give enthusiasts enough time to ponder, extrapolate and "figure" this one out. There are no tricks in this question. 

If nobody gets it, then that's that.  I will not be posting the answer.  It would deflate & detract from the power of this "stunner" as an examination " bypass-all-24-questions-but-if-you-attempt-and-get-#25-correct, you-score 100% on-the-exam"  type of power!  Just sheer poetry to me!  

Degree of difficulty 4+ .... out of a maximum of  4       

Level 10:

Without the use of logarithmic and/or trignometric tables, sliderules, calculators, computers etc., and starting from first principles, prove the following:

cot 7½°  =  √2 + √3 + √4 + √6

<{POST_SNAPBACK}>

<{POST_SNAPBACK}>

Tried to remove original message... formatting looked okay when I wrote it, but went awry when viewed in html

Anyway, nevermind.... I didn't prove anything

Edited April 8, 2005 by Eman

[lampard10]

It's way over my head.

1 chang + 1 archa + 1 leo = ฿165

Now I understand that

[chuchok]

It's way over my head.

1 chang + 1 archa + 1 leo = ฿165

Now I understand that

<{POST_SNAPBACK}>

Exactly! I think I'll pop out now and watch some grass grow.