Recreational Mathematics
 

I think we have a full quorum of geeky nerds in here, so this thread might work.

Post your math(s) related ramblings here. Discuss, comment, dispute or drift at your discretion.


I'll go first.


So, a few nights back, unable to sleep, I tried counting sheep. I started getting turned on so I figured something different was needed. I had a little meander through mathematics and although I'm sure it is nothing new or revolutionary, it's mildly interesting so I'll share it here.

I wondered, are there any numbers which are both cubes and squares? In the sense that 16 is square (4x4) and 27 is cubic (3x3x3).

First I thought of 1,000,000 which is 100 cubed and 1,000 squared. Done.

Then I started going through the squares to see if any were cubes. The first I found was 64, being 4 cubed or 8 squared.

Then I noticed that 100 and 1,000 are in a 1:10 ratio, 4 and 8 are 1:2. I wondered, does 1:[any integer] deliver a cubic square?

I tried 3 and 9, but that didn't work (3^3=27, 9^2=81).
Then I tried 9 and 27. 9^3 and 27^2 both = 729.

Ah, so it should work not with 4 and 16, but with 16 and 64. Yup, 4,096.

By this time I saw the general pattern that was going on.
Take a starting number, x. Square it, and let that be the number that gets cubed. Meanwhile, cube x, and let that result be the number which gets squared.

x^2^3 = x^3^2 = cubic square. Also = x ^6, FTR.

Well, of course, now that I see it. Take x, cube it, then square that, and the result will be a cubic square. Well, duh.

It's kind of obvious once you see it, and that is the beauty of this kind of maths. I started with a question I wasn't sure about, and pretty soon, just by reasoning, had not just found an answer (yes) but had understood how these numbers worked, and had a formula for making as many as I want.

Then, because I am actually a liberal arts graduate, I wrote a haiku about this.

Are there cubic squares?
The square of x cubed equals
the cube of x squared.


Final question for discussion: are there any cubic squares other than those described by the x^2^3 formula?

--snip--
AGREED!

Yes.

Yeah, but apart from us.

5!

I've heard warm milk works.

Zen, you are so hot right now.

Here are two: 1 and i
The fallacy for i is that it depends on the order of operations

... like clockwise or counter-clockwise for the hunter and the squirrel.

;)

chilled Vodka works better

I had this dream once and there was like this "planet of numbers"... I said to my self I kept waiting for the signal but it never came.. and then this little oriental guy poped up and said 5-9-10..

:zzz:

n = 10000
;
loop i (1,n)
...loop j (1,n)
......;
......x_square = i^2
......x_cube = j^3
......;
......if x_square = x_cube
.........print i
.........print x_square
......end_if
...end_loop
end_loop
end
store


Results:

x_ = 1
x_square = 1

x_ = 8
x_square = 64

x_ = 27
x_square = 729

x_ = 64
x_square = 4096

x_ = 125
x_square = 15625

x_ = 216
x_square = 46656

x_ = 343
x_square = 117649

x_ = 512
x_square = 262144

x_ = 729
x_square = 531441

x_ = 1000
x_square = 1000000

x_ = 1331
x_square = 1771561

x_ = 1728
x_square = 2985984

x_ = 2197
x_square = 4826809

x_ = 2744
x_square = 7529536

x_ = 3375
x_square = 11390625

x_ = 4096
x_square = 16777216

x_ = 4913
x_square = 24137569

x_ = 5832
x_square = 34012224

x_ = 6859
x_square = 47045881

x_ = 8000
x_square = 64000000

x_ = 9261
x_square = 85766121



You can find the pattern
:p:

Back in the late 50's, when there were only 600 million living Chinese,
my "Can't get to sleep" problem was...

What is the total number of people who have every lived on earth ?

But now, all you have to do is a Google search, and you get this

NUMBER WHO HAVE EVER BEEN BORN 107,602,707,791

Number of people who are worth a shit 150




give or take

Even the title of this thread makes me anxious. I do the maths if I need them, but childhood trauma prevents ever attaching recreation to them.

Counting...

Lamplighter, it's true that 1 is a cubic square, but I think 1 is described by the x^2^3 formula.

Bruce ... :lol: yours? Congratulations. :D

http://www.cellar.org/showthread.php...801#post835801

I note that there are some that are exactly two things, some that are exactly three things, one that is exactly seven things, but none that are exactly one thing, none that are exactly four things, none that are exactly five things and none that are exactly six things.

What Griff said.

http://www.cellar.org/showthread.php?t=25982

This is Zen keeping it stiff.

Animation of zooming into the Mandelbrot set to a magnification of 2.1 x 10^275.

Who are you, Cliff Pickover. :haha:

How could there be?

Find any cubic square number. cube-root then square-root it. then quare and cube that solution, and it will have to be the same. it will HAVE to follow the x^2^3 formula.

I'm *pretty sure* that you are right, but I was wondering about a situation where x^3 = y^2 where x and y are not related in this way.

Something like 7^3 and 19^2, although of course not that.

But yeah, I don't think there can be.

With very good reason.

well, MY dad used to just hit me.

Had the same effect, and indirectly, the same cause.
Of course there was the additional problem of him feeling inferior to someone as smart and attractive as you.

U so funny.

I love you long time.

:heartpump

Barbie said math is hard. Some people even believe philosophies taught by a doll.

Which proves a serious need for iconoclasts.

Why study math when they'll never use it ?

YOU try cooking for the entire village hunting party's return. How am I supposed to know how much lard to use when I usually only cook for my brood of 12?

Actually it would be math teachers without "soft" or basic human skills, who make math hard. I learned it whenever I needed it, but was programmed by math teachers very early on to never enjoy it.

Odd how different experiences can be...

My Junior year high school math teacher turned me on to mathematics.
He also taught Biology and Chemistry, but I don't remember which years those were,
but I remember them classes as "good" classes.

In today's vernacular I guess he would just be called a "good teacher".

That's just arithmetic. Divide the number of people in the hunting party by 12 and multiply the result by the amount of lard you normally use and voila!

REAL math always has something spatial hidden away in it, like trying to figure out the area under a curve or those bizzare calculus problems where you are supposed to buy into the concept of X approaching infinity. How the hell do you "approach" infinity, anyhow? And why would you want to?

Or the stupid geometric proofs that almost caused me to drop out of the 10th grade. If I hadn't gotten my Dad to do most of my geometry homework for me, I'd be just another high school dropout standing on a street corner with a sign reading, "Will work for mind altering drugs." Oh wait! I already do that. Never mind.

My point is that it's a well known fact that women have no spatial abilities. Therefore we should stay away from stuff like math and geometry and calculus, and you certainly shouldn't leave camp with any hunting parties. Why, who knows where you might end up wandering off to? Just tend to that cooking fire, woman. ;)

Sam, I thought you already answered those questions (elsewhere) :rolleyes:

Yeah, I'm just full of profound statements. Ask anyone. :p:

My middle school daughter just turned me on to this nerdtastic math channel on youtube. A day late, but here's some mathed potatoes.

One potato, two potato, three potato, four,
five potato, six potato, seven potato more.
Icha bacha, soda cracker,
Icha bacha boo.
Icha bacha, soda cracker, out goes Y-O-U!


You're it ! ;)

Attachment 41980

Like, whoaaah, man.

Oh and

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321

Cosmic, man.

Hmm

and

Japanese multiplication method

Attachment 42457

ETA:

Please demonstrate 1 * 10

Or other factors with a digit zero

Eta. Also, whoa!

Honorabu Big-B-san

Easy to draw inbisibru rine to represent zero. Just not to forget where draw it. Has no intersections.

Prease to remember, "zero" is name of fighter prane make during war, arso call "frying coffin". Traumatic memories, prease not to mention to chirdren.

Zensei.

[quote=ZenGum;847990]Japanese multiplication method


Attachment 42457

This is an interesting illustration.
But I doubt adults use the the method.
It's sort of like kids adding by counting on their fingers.
It's also what we do in algebric multiplication of polynomials...


Attachment 42479

but then if, as Big V asks, what happens with zero's, we leave gaps in the summation:

Attachment 42478

missa Zensum ... fer usir

"What, you don't recognise Latin numerals?"

of course not! He's an American!

Americans know what Romain numerals are; how else do you think we know which Rocky squeal is which?

Meh, they didn't even have a zero. That's nulla good.

The zero is indeed a brilliant invention.

Which reminds me, why is Halloween equal to Christmas?

My Google skills are almost as good as 3foot's. http://cellar.org/2012/bwekk.gif

Here's a good one. And solution.

An invention of pessimists.

Not quite.

Let's say you have zero cancer. That would be good, right?

Or zero court summons, or zero traffic tickets...

I could go on you know.

I don't understand this...I mean your answer. I don't get it. What's with all the magic symbols, etc?

Why IS Christmas like Halloween? All your mathematics don't tell me a thing.

All it really says is that the number 25, when converted to base 8, is written 31. They could just as easily ask why is St. Patrick's Day (17) like Martin Luther King Day (21, at least this year,) or why is Valentine's Day (14) like Emancipation Day (16)...

yeah.


I really don't belong in the math thread.

But that's where all the hot nerds hang out.

Wait till I tell you about the drag and drop image search...:rotflol: