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?

ZenGum;835650 wrote:

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

--snip--
AGREED!

ZenGum;835650 wrote:

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

Yes.

Yeah, but apart from us.

5!

I've heard warm milk works.

Zen, you are so hot right now.

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

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.

;)

glatt;835678 wrote:

I've heard warm milk works.

chilled Vodka works better


[YOUTUBE]gZEdDMQZaCU&start=2[/YOUTUBE]

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?p=835801#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.

Griff;835788 wrote:

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.

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.

[YOUTUBE]0jGaio87u3A[/YOUTUBE]

Who are you, Cliff Pickover. :haha:

ZenGum;835650 wrote:

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

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.

Ibby;836373 wrote:

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.

Griff;835788 wrote:

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.

With very good reason.

A new study by researchers at the University of Chicago has found that for people who get anxious at the idea of doing mathematics, just preparing to do a math problem can trigger activity in a part of your brain that registers physical pain.

xoxoxoBruce;839699 wrote:

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.

xoxoxoBruce;839800 wrote:

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

For someone who has math anxiety, the anticipation of doing math prompts a similar brain reaction as when they experience pain—say, burning one’s hand on a hot stove.

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?

tw;839839 wrote:

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

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".

infinite monkey;839845 wrote:

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?

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. ;)

How the hell do you "approach" infinity, anyhow? And why would you want to?

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

Lamplighter;840219 wrote:

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.
[YOUTUBE]F5RyVWI4Onk[/YOUTUBE]

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 ! ;)

[ATTACH]41980[/ATTACH]

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

[ATTACH]42457[/ATTACH]

The lines and numbers above may not make any sense at first, but according to William C. at Themetapicture.com: "The lines over the circles are color coded. notice the single red line and 3 blue lines representing "13" group together while the single green and 2 black lines take their own group. [Simply] draw your first group of lines in one direction then your second group of lines going over the first, count the groups of intersections and there's your answer."

ETA:
[youtube]e-P5RGdjICo[/youtube]

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


[ATTACH]42457[/ATTACH]

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...


[ATTACH]42479[/ATTACH]

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

[ATTACH]42478[/ATTACH]

missa Zensum ... fer usir

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

ZenGum;849040 wrote:

"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?

ZenGum;849040 wrote:

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

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?

We have Christmas on 25 December. Let’s put that here:
DEC 25
= 25 [let's focus on the day, ok?]
= 24 + 1 [it's obvious I know...]
= (8^1) * 3 + (8^0) * 1 [some fancy arithmetic]
= 31 [of base 8. Much easier to work with than base 3]
= OCT 31 [let's use the short form of octal]

Wait a minute, OCT 31 looks awfully familiar… Hey it’s Halloween, which falls on 31 October! Thus is Christmas equal to Halloween.

My Google skills are almost as good as 3foot's.

Here's a good one. And solution.

ZenGum;850118 wrote:

The zero is indeed a brilliant invention.

An invention of pessimists.

Griff;850176 wrote:

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.

xoxoxoBruce;850124 wrote:

My Google skills are almost as good as 3foot's.

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.

xoxoxoBruce;850124 wrote:

My Google skills are almost as good as 3foot's.

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

Trilby;850179 wrote:

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.

Clodfobble;850185 wrote:

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)...

Bitch bitch bitch, it's the mathematical answer to Zen's question.
Hey, look at the top of the thread, does it say Philosophy? Noooooooooo, it says Mathosophy. :p:

Clodfobble;850185 wrote:

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)...

A bit more than that. 25 in decimal, which can be abbreviated to DEC 25, is equal to 31 in octal, or OCT 31.

ohferchrissakes.


Why is a writing desk like a raven?

answer me that one and I'll be impressed.

Happy Monkey wrote:

A bit more than that. 25 in decimal, which can be abbreviated to DEC 25, is equal to 31 in octal, or OCT 31.

Oh that's true! I didn't notice that part. I'm used to seeing it written 31[size=1]8[/size], with a little subscript 8.

Trilby;850317 wrote:

Why is a writing desk like a raven?

Because Poe wrote on both.

Lewis Carroll wrote:

"Because they can produce a few notes, tho they are very flat; and it is nevar put with the wrong end in front!" This, however is merely an afterthought; the Riddle, as originally invented, had no answer at all.

Other answers (all from this awesome book):

Sam Loyd wrote:

because the notes for which they are noted are not noted for being musical notes

Aldous Huxley wrote:

because there is a 'b' in both, and an 'n' in neither.

David B. Jodrey, Jr wrote:

Both have quills dipped in ink.

Cyril Pearson wrote:

Because it slopes with a flap.

Ha! I even have that book (the Annotated Alice) but haven't looked at it in years and years. got it when I was in my teens!

Read it! I would probably say it is my favorite book. Some of the notes added in the most recent addition aren't all that great, but all of the original annotations are fascinating.

Clodfobble;850329 wrote:

Oh that's true! I didn't notice that part. I'm used to seeing it written 31[size=1]8[/size], with a little subscript 8.

I'm used to seeing it written 31[size=1]8[/size], with a little subscript 8.

I'm used to seeing it written

How far apart our worlds are. I've never even heard of it until now.

aaa
aae
aai
aao
aau

aea
aee
aei
aeo
aeu

aia
aie
aii
aio
aiu

aoa
aoe
aoi
aoo
aou

aua
aue
aui
auo
auu

eaa
eae
eai
eao
eau

eea
eee
eei
eeo
eeu

eia
eie
eii
eio
eiu

eoa
eoe
eoi
eoo
eou

eua
eue
eui
euo
euu

iaa
iae
iai
iao
iau

iea
iee
iei
ieo
ieu

iia
iie
iii
iio
iiu

ioa
ioe
ioi
ioo
iou

iua
iue
iui
iuo
iuu

oaa
oae
oai
oao
oau

oea
oee
oei
oeo
oeu

oia
oie
oii
oio
oiu

ooa
ooe
ooi
ooo
oou

oua
oue
oui
ouo
ouu

uaa
uae
uai
uao
uau

uea
uee
uei
ueo
ueu

uia
uie
uii
uio
uiu

uoa
uoe
uoi
uoo
uou

uua
uue
uui
uuo
uuu

***

Counting in base 5, inspired by another thread.