Thursday, October 20, 2005

144

I don't mean to make two posts in a row geeky, but I was so inspired tonight to write about a very cool (er, square) number.

144 is my favorite rational number. BTW, phi is my favorite irrational number for anyone dying of curiosity. But back to 144.

Why do I think 144 is such a neat number? Well. . .

(1) 144 is a perfect square - 12x12, a dozen dozens, a gross
(2) The digits of 144 are 1 and 4, also both perfect squares
(3) Add the digits of 144 - 1 + 4 + 4 = 9 - also a perfect square
(4) Multiply the digits of 144 - 1x4x4 = 16 - also a perfect square
(5) Flip around 144 to get 441, also a perfect square - 21x21 = 441
(6) 4 and 36 are both perfect squares and 4x36 = 144
(7) 9 and 16 are both perfect squares and 9x16 = 144

There you have it! Isn't 144 a very cool (er, square) number?

Yes, I admit that I am a math geek. Note I said "math geek", not "math nerd", or "math dork." The latter two do not make sense. A pity the terms nerd, geek, and dork are so often misused. . .

I have to blame my obsession with 144 on my dear sister Hannah. She has explained the intricacies of that fine number to untold numbers of poor captive victims. Few of her friends have not had to sit through a "144 talk." :) I love my sister.

23 comments:

Hannah :-) said...

Hey! They weren't victims... they enjoyed it... at least, I think that's what a blank expression followed by a few moments of silence means.

Adrian C. Keister said...

Oh, you two are such a trip.

Phi is the Golden Ratio, right? That is an incredibly interesting number. Incidentally, the word is pronounced \FEE\, not \FAI\, as so many of my physics teachers so wrongly pronounce it. I'm studying Greek right now, and my brother Lane is a Greek scholar. It's \FEE\.

The Golden Ratio is related to all sorts of things: the Fibonacci sequence, the Parthenon, high heels, climaxes in novels and in music, and so on.

In Christ.

Esther said...

Um, oooookay! Interesting. ;)

I THOUGHT I was Hannah's friend but she's never explained 144 to me. :-/ On second thought, that's really okay with me! Our friendship is strong enough without having to enjoy such a bonding time discussing the "perfectness" of 144.

You girls are absolutely crazy, but I still love you both despite this fondness for math which I just cannot fathom. ;)

Susan said...

How has Hannah managed to neglect this area of your friendship, Esther? Wow, it must have been an oversight on her part. I'll have a "big sister" talk and straighten this out. I expect an apology will be forthcoming.

Just to clarify, 144 is not perfect, as you stated, Esther. You see, a perfect number is a number whose factors (other than itself) add up to that number. For example, 6 is the first perfect number since its factors (other than 6) are 1, 2, and 3, which sum to 6. Similarly 28 is the second perfect number, since its factors (other than 28) are 1, 2, 4, 7, and 14, which sum to 28. Since I know you are aching to know the third perfect number, I'll go ahead and tell you it's 496, but you have to justify it yourself.

I just couldn't resist. . . ;)

Actually Hannah has so influenced Summer concerning 144 that she just wrote a short essay on 144 to explain why she loves math. In the essay she called 144 a perfect number, and we did have to correct her. . .

Ashley said...

I like 26. For no reason other than it's the day I was born. :-)

Susan said...

Yes, Phi is a fascinating number. I did a project on Phi in college. The connection to the Fibonacci sequence was possibly the most interesting to me, and the relation to music and stories the most bizarre.

www.goldennumber.net is a very cool site, even if they mispronounce phi with their clever pun. . .

Funny you should mention the pronunciation, Adrian. I have wondered the correct pronunciation, as I've heard it both ways, the incorrect pronunciation being more prominent. When I took Calculus II and III from my dad at the local community college I remember him expressing unsurety as to the correct pronunciation, although he did most often pronounce it "fee."

Hannah :-) said...

Haha, notice that you (Susan) posted that last reply at the wonderful time of '1:44'! :-)

Esther, I am so sorry that I deprived you of the joy of knowing about 144. I appreciate you being so gracious as to not hold that against me. You are very forgiving. :-)

Susan said...

It gets better. . .

My dad had some extra time on his hands today and discovered that, get this, the 12th Fibonacci number is 144, which is of course 12x12. Is that cool or what?! More on this night's discoveries about the Fibonacci sequence in a future post on Phi and Fibonacci :-D.

BTW, my last posting time of 1:44 (which Hannah was astute to notice) was completely by accident, unplanned, and unaltered. What is the chance?

Susan said...

It gets better. . .

My dad had some extra time on his hands today and discovered that, get this, the 12th Fibonacci number is 144, which is of course 12x12. Is that cool or what?! More on this night's discoveries about the Fibonacci sequence in a future post on Phi and Fibonacci :-D.

BTW, my last posting time of 1:44 (which Hannah was astute to notice) was completely by accident, unplanned, and unaltered. What is the chance?

Susan said...

Hmmm... very strange. I don't entirely understand computers.

My first post on the 12th Fibonacci number did not register on my blogs main page until I reposted it just now. Now the old post and the new one both are accounted for and I just got e-mail confirmation for both at the same time even though the first post was 16 hours earlier than the second.

The first post did show in the comments before, just not in the number on the main page or in the permalink. Odd.

Susan said...

Insert "comment" for "post" on previous comment. . .

Ben Garrison said...

8128

1) the 4th perfect number. (4 is a power of 2)
2) composed only of powers of 2.
3) contains the 2nd perfect number (28) - also an ordinal power of 2.
4) 128 is also a power of 2.
5) 81 is 3^4 (the exponent is a power of 2)
6) is composed of 4 digits (also a power of 2)
7) if you multiply all of the digits together, you get 128, which is a power of 2, and is also contained within the number.
8) including this, I have listed 8 cool things about it, which is a power of 2.

Susan said...

haha, ok, your number wins. . .

Hannah :-) said...

NO! I will never forsake 144. You can if you want to, Su. Be a traitor. I will be faithful.
144 wins!!!!!!
But yours is a cool number too, Ben. :-)

Ben Garrison said...

Look at it this way, Hannah...your number's uniqueness deals with numbers to the power of 2. Mine deals with 2 to the power of numbers.

So which is cooler? N^2 or 2^N? I would argue that 2^N is clearly cooler. 2^N is the realm of the unsolvable, computationally speaking. 2^N is the line between the polynomial and the exponential. N^2 says "my second derivative is constant. A rut in the graph of life." 2^N screams "derivatives, you cannot defeat me. I will rise above you, unless you be infinite in number"

Hannah :-) said...

Let me put it this way - 144 is more friendly and loveable. It's smaller, prettier, and the uniqueness and complexity of 144 is easier to understand and explain. Like mom said, "I can explain the depth of 144 to my algebra 1 students, but they probably wouldn't understand the depth of 8128."
So, there's a homey, friendly, knowable feeling to 144 with a little awe mixed in. He even drops in twice a day!
Then there's 8128, which inspires more awe. It's not as easy to grasp, and some of its meaning possibly exceeds what my mind can completely understand. 144 is a friend; 8128 is an esteemed acquaintance.
So, on regular days, I'll enjoy the comradery I share with 144. On days when I feel like breaking out of the norm and reaching to greater heights, I will turn my thoughts toward 8128.

Ben Garrison said...
This comment has been removed by a blog administrator.
Ben Garrison said...

Like an ignorant child who wants to go on making mud pies in a slum because you cannot imagine what is meant by the offer of a holiday at the sea, you are far too easily pleased.

Hannah :-) said...

Ho-hum, I'm just over here enjoying my mud pies... anybody wanna pway?

Ben Garrison said...

After some introspection, I realize that you have a valid point, due to 144's uniqueness as the last perfect square fib. number.

I still stand by my assertions, however.

Esther said...

Okay, all those numbers gave me a headache - where's the asprin I never take?! ;-)

Adrian C. Keister said...

Hmm. What should be my number? Well, besides the number 8, which has the surely incidental advantage of being infinity on its side.

I remember Ramanujan talking with G. H. Hardy one time. Hardy mentioned that the number 1729 had no interest whatever. And Ramanujan immediately countered, "It is a very interesting number. It is the smallest number expressible as the sum of two [positive] cubes in two different ways."

That has to be an interesting number. Incidentally,

1729 = 1^3 + 12^3 = 9^3 + 10^3.

Now the rest of the posts here, Esther's excepted, must all be a contest of geekiness.

In Christ.

Susan said...

Haha, my dad had already claimed that number for that very reason :). I guess you both can share.