Count As High As Possible Before A Mod/Admin Posts

[Valkyrie]

*sulks*  Here's a cheesecake for the Down-Under Wonder.  (The having two teenage boys gets you sympathy points.  Besides, I don't want you siccing them on us ) 

 

THREE

 

[Drew Espinosa]

Thanks @Valkyrie for adding the 4 to pi!

 

Now, where was I? Oh yes, Four!!!  

3.141

Edited April 10, 2017 by Drew Espinosa

[Defiance19]

Hi Five! 

[Drew Espinosa]

SIX!!! One letter off from another word...  

 

3.14159

Edited April 10, 2017 by Drew Espinosa

[Valkyrie]

Just now, Drew Espinosa said:

SIX!!! Rhymes with...  

 

3.14159

Six rhymes with angel?   

 

Seven 

[Drew Espinosa]

Eight... the number of legs for an evil creature!

 

3.1415926

Edited April 10, 2017 by Drew Espinosa

[Defiance19]

Nine

 

Off to make dinner. May the force be with you 

Edited April 10, 2017 by Defiance19

[Drew Espinosa]

Hmm... Graeme did say;

Quote

The more fun the comments, the more likely I'll be to read and not post.

 

With that in mind...

...have fun reading!

Quote

Today, we know π to well over the trillionth decimal place. It is a number that has shown up throughout mathematics, so it is no surprise that mathematicians have been dealing with the number for millennia.

 

The mathematicians of the Ancient world observed that the circumference of a circle was just over three times the diameter. So, they set out to estimate the value of π… and began a centuries long journey to take π from being “just over 3” to “3.14159265... etc.”

 

Throughout the world, various methods were devised to approximate π, however, the one I’ll be focusing on is the method developed by Archimedes.

 

He knew that the perimeter of an inscribed polygon would be less than the circumference, and the perimeter of a circumscribed polygon would be greater than the circumference.

 

So, he used this principle to work out a way in approximating π. He inscribed a hexagon on a circle, calculated the lengths of the hexagon’s sides, and then calculated its perimeter. He then doubled the sides of that hexagon, to get a dodecagon. And repeated the process of calculating its side length and perimeter.

 

And he repeated that process for a 24-gon, then a 48-gon, and finally a 96-gon.

 

Ah, but wait! He wasn’t done, because he then circumscribed a hexagon on the circle, and repeated the entire process. Archimedes was able to calculate the perimeters as 223/71 for the inscribed 96-gon and 22/7 for the circumscribed 96-gon.

 

Meaning, π was somewhere in between those two numbers, or in mathematical notation:

 

223/71 < π < 22/7

 

And since both fractions begin as 3.14 in decimal form, Archimedes found the first three digits of π.

 

 

******

 

While Archimedes, was the first to use this method, he certainly wasn’t the last. Which brings us to Ludolph van Ceulen, a Dutch mathematician from the 16th Century.

 

This man gave the most accurate approximation of π up to that point, all thanks to Archimedes’ method.

 

The only difference was that he started with a square, instead of a hexagon.

 

The following is to give you an idea of what he did:

 

 

 

First, consider the circle above. We will be inscribing and circumscribing polygons on it.

 

 

 

The perimeter of the inscribed square is about 2.83, and that of the circumscribed square is 4. Which gives us the first inequality:

 

2.83 < π < 4

 

 

 

The perimeter of the inscribed octagon is about 3.06, and that of the circumscribed octagon is about 3.31. Which gives us the second inequality:

 

3.06 < π < 3.31

 

 

 

The perimeter of the inscribed hexadecagon (16-gon) is about 3.12, and that of the circumscribed 16-gon is about 3.18. Which gives us the third inequality:

 

3.12 < π < 3.18

 

As you can see, these inequalities hone in on π, eventually getting the digits of π as you continue doubling the sides of the inscribed and circumscribed polygons.

 

As for van Ceulen, he doubled the sides until he had 2⁶²-gons. And with that, he found π to the first 35 decimal places:

 

3.14159265358979323846264338327950288

 

This was an impressive achievement. So impressive in fact, that for a time, π was called the Ludolphine Number in Germany.

 

 

******

 

Of course, this record would be surpassed over the next couple centuries, when mathematicians began using infinite series to find π (where before they could only find tens of digits, they could now find hundreds).

 

And those records were broken during the last several decades, thanks to computers, and we now know π to well over a trillion decimal places.

 

We have certainly come a long way.

 

If you have any questions, I’ll be happy to answer them. 

 

TEN!!!

Edited April 10, 2017 by Drew Espinosa

[Valkyrie]

He said 'fun' comments, @Drew Espinosa Now he's definitely going to set us back to zero.  

 

ELEVEN

[Drew Espinosa]

Anything math-related is automatically fun.

 

3.14159265358

^twelve digits of pi!  

Edited April 10, 2017 by Drew Espinosa

[Valkyrie]

 Nope.  Sorry.  LOL  

 

My next door neighbor is mowing his lawn and the cats think it's Armageddon.  lol  

 

Thirteen

[TalonRider]

That cheese cake would be a diabetics dream.

 

Back to Zero.

[Drew Espinosa]

Fourteen!!!

 

3.1415926535897

 

When life gives ya lemons, make lemonade!

I have a number, n, and I'll use your zero, BOP, to raise it and get 1!  

Edited April 10, 2017 by Drew Espinosa
clarification

[Valkyrie]

*throws the cheesecake at the bad Birdy*   Don't you have a shiny to steal?  

 

TWO (I'm counting Drew's post as one)  

[Drew Espinosa]

3.14

three!  

[wenmale64]

oooh,  I get to beat them all to the------    TEN   again       Oops  I'll try four

Edited April 10, 2017 by wenmale64

[Valkyrie]

Three, FOUR, shut the door (on BOP and any other mod/admin that wants to derail our progress)   

 

Damn, @wenmale64 spoiled my rhyme (you were four, BTW)  

 

FIVE and feelin' alive!

Edited April 10, 2017 by Valkyrie

[wenmale64]

I'll take SIX for pics

[Drew Espinosa]

Naughty pics?

Seven Deadly Sins!

Edited April 10, 2017 by Drew Espinosa

[Timothy M.]

Eight ?

Why am I doing this? We're not getting anywhere.  

[Valkyrie]

Now that sounds like our drewbear...

 

Why was six afraid seven?  Because seven EIGHT nine!  

 

Aw man... my joke was spoiled...

 

NINE

Edited April 10, 2017 by Valkyrie

[wenmale64]

OK NOW I get  TEN

[Drew Espinosa]

8 minutes ago, Valkyrie said:

Why was six afraid seven?  Because seven EIGHT nine!  

Aw! You made a math pun!

 

8 minutes ago, Valkyrie said:

Now that sounds like our drewbear...

 

 

8 minutes ago, Timothy M. said:

Eight ?

Why am I doing this? We're not getting anywhere.  

Aw, Tim, we got to 31 awhile ago.

 

Oh, and... ELEVEN!!!  

Edited April 10, 2017 by Drew Espinosa

[Valkyrie]

Eleven pipers piping...   Everyone now picture Scottish men clad in kilts...  

 

Twelve drummers drumming!  

[wenmale64]

How about an even dozen?   Twelve

Make it a bakers dozen---  thirteen

Edited April 10, 2017 by wenmale64