mrimer
Level: Legendary Smitemaster

Rank Points: 5056
Registered: 02-04-2003
IP: Logged

Tscott wrote:
I think it's better to say ω is the set of all finite ordinals {1,2,3,...}.

As opposed to the infinite ordinals, right? I just read about these so-called "supernatural" numbers in Godel, Escher, Bach. And...heh...in case someone is wondering, they're called supernatural not because mathematicians aren't sure whether they really "exist" or not, but because they're larger than all the natural numbers.

____________________________
Gandalf? Yes... That's what they used to call me.
Gandalf the Grey. That was my name.
I am Gandalf the White.
And I come back to you now at the turn of the tide.

Donny
Level: Delver
Rank Points: 40
Registered: 11-01-2004
IP: Logged

Wow. This thingy really go haywire.


____________________________
"If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?"

David Hilbert (1862-1943)

wackhead_uk
Level: Smiter

Rank Points: 352
Registered: 06-21-2004
IP: Logged

Let's wrap this thread up with a nice smilie to explain it all:



[Edited by wackhead_uk at Local Time:01-07-2005 at 08:43 PM]

Tscott
Level: Smiter

Rank Points: 382
Registered: 02-10-2003
IP: Logged

Hey yeah. It's this thread again.

I've got some free time for reading this summer and I've found a few good math books (and one science) to recommend.

First I'm halfway through A Short History of Nearly Everything by Bill Bryson and WOW!!! This is book is mind blowing, funny and scary (often all three at once). It takes a look at everything scientist currently know about our world, the universe and the stuff they're made of. It also goes into how do we know this stuff- when they say the Earth weighs 5.9725 billion trillion metric tons, who weighed it and how? It also goes into who discovered what, and then who got credit for discovering it. It does a great job of providing awe and wonder at just how lucky and fragile our existence is. Highly recommend for anyone who has a passing interest in any and all areas of science.

I'm also halfway through The Secret Life of Numbers by George G. Szpiro. The perfect 'bathroom' book for someone in math, short chapters, interesting tidbits, but doesn't go into any depth at all.

Also planned for my summer reading, Algebra Unplugged and Calculus for Cats, both by Kenn Amdahl and Jim Loats, PhD. They're both books that explain their topic in plan, fun language. I've only glanced at these briefly, but they look like they cover the basics in an easy to approach manner. If you're taking an Algebra or Calc course and want to get the most out of it, you'd do well to read one of these along with the text.

(Now if only I could find a book like these on Trigonometry. Anyone know of any?)

And in my last post in this thread I mentioned I was thinking of getting The Language of Mathematics by Keith Devlin. I did. It's great. It really helped me when I took my Math content area test. This book explores perspective in art, topology, probability, calculus, prime numbers, stacking problems and more. A great overview of the basics of a lot of areas of math. It does a good job explaining all the concepts and the math knowledge needed to understand is only high school level, so anyone should be able to enjoy this one.

And rereading this thread I see I never got around to The Penguin Book of Curious and Interesting Numbers which I had intended to. Looks like I better add that to my list.

____________________________
And I can recall our caravel: a little wicker beetle shell with four fine maste and lateen sails,
its bearings on Cair Paravel. O my love, O it was a funny little thing to be the ones to've seen.
-Joanna Newsom "Bridges and Balloons"

---

[Last edited by Tscott at 06-10-2006 09:15 AM]

MeckMeck GRE
Level: Smitemaster
Rank Points: 594
Registered: 01-03-2005
IP: Logged

I can recommend some books of Martin Gardner.

I don´t know their English names, but in German they are "Mathematischer Zirkus" and "Mathematische Hexereien" and so on.

Those books are about interesting problems involving 0, nothing, infinity, faculties, möbius bands, combinatory, game theorie,logics, and so on.

RoboBob3000
Level: Smitemaster

Rank Points: 1978
Registered: 10-23-2003
IP: Logged

I just graduated from college with a degree in applied mathematics a couple of weeks ago, and for a graduation gift, my mom got me a copy of a book titled Letters to a Young Mathematician by Ian Stewart. The book is exactly what the title sugggests. It's a collection of letters from a math professor to an imaginary student considering pursuing her studies in math. I haven't read much of it yet (been busy moving back to the Seattle area and, well, doing a lot of goofing off), but when I complete it I'll share more of my thoughts about it.

____________________________
http://beepsandbloops.wordpress.com/

---

[Last edited by RoboBob3000 at 06-10-2006 09:30 PM]

miketo
Level: Delver

Rank Points: 61
Registered: 01-04-2006
IP: Logged

mrimer wrote:

ErikH2000 wrote:
I really love this book. If I am feeling tired and world-weary, it is a wonderful thing to pick up and read.

I'm with you here. I also enjoyed the "sequel", What do you care what other people think?

I recommend both books, very highly. Great reading.

---

[Last edited by Oneiromancer at 06-11-2006 07:18 PM : added closing quote tag]

coppro
Level: Smitemaster
Rank Points: 1308
Registered: 11-24-2005
IP: Logged

miketo wrote:

mrimer wrote:

ErikH2000 wrote:
I really love this book. If I am feeling tired and world-weary, it is a wonderful thing to pick up and read.

I'm with you here. I also enjoyed the "sequel", What do you care what other people think?

I recommend both books, very highly. Great reading.

Please close the quote tags - it's more readable that way.

As for the topic, I'm having a blank as to what books are good reading .

---

[Last edited by coppro at 06-11-2006 07:51 PM]

Oneiromancer
Level: Legendary Smitemaster

Rank Points: 2936
Registered: 03-29-2003
IP: Logged

Coppro, please try to be more diplomatic when pointing out other people's formatting errors.

Game on,

____________________________
"He who is certain he knows the ending of things when he is only beginning them is either extremely wise or extremely foolish; no matter which is true, he is certainly an unhappy man, for he has put a knife in the heart of wonder." -- Tad Williams

coppro
Level: Smitemaster
Rank Points: 1308
Registered: 11-24-2005
IP: Logged

Oneiromancer wrote:
Coppro, please try to be more diplomatic when pointing out other people's formatting errors.

Game on,

Sorry. The two were intended to be seperate sentences. The second was actually talking about me having read some really good books, then having forgotten them.

Apologies.

Watcher
Level: Smitemaster

Rank Points: 902
Registered: 02-04-2003
IP: Logged

Tscott wrote:
And in my last post in this thread I mentioned I was thinking of getting The Language of Mathematics by Keith Devlin. I did. It's great. It really helped me when I took my Math content area test. This book explores perspective in art, topology, probability, calculus, prime numbers, stacking problems and more. A great overview of the basics of a lot of areas of math. It does a good job explaining all the concepts and the math knowledge needed to understand is only high school level, so anyone should be able to enjoy this one.

I haven't read that one, but I've read two other Devlin books: Mathematics: The New Golden Age and Mathematics: The Science of Patterns. It's been some time since I last read them, but I recall that they were quite enjoyable. Golden Age is about significant recent developments in math ("recent" meaning "during the last 50 years"), whereas Patterns tries to give an overview of the many branches of math and what they have in common.

Also, I second the recommendation of Feynman's books. Incredibly entertaining.

____________________________
Today the refrigerator, tomorrow the world!

miketo
Level: Delver

Rank Points: 61
Registered: 01-04-2006
IP: Logged

Please close the quote tags - it's more readable that way.

No offense taken. I was in a hurry and lacked time to make the post more legible.

coppro
Level: Smitemaster
Rank Points: 1308
Registered: 11-24-2005
IP: Logged

And now it comes to me. The Music of the Primes by Marcus du Satoy is a great book about prime numbers and the Riemann Hypothesis.

skell
Level: Legendary Smitemaster

Rank Points: 3734
Registered: 12-28-2004
IP: Logged

Like somebody mentioend before I recommend all Smullyan's Books. I have personally three of them:
The lady or the Tiger
The riddle of Scherezade
What is the Name of this Book?
All are great, and I always return to them :-).

And btw, I don't think somebody mentioned it before, but there is a way to prove, that it is possible to create a triangle with two right angles (90 degrees). How?

According to the "The riddle of Scherezade", there is mathemetacial rule which goes like that:
0.99999...=1 , because:
x=0.99999... /*10
10x=9.99999...
10x-x=9.99999...-0.99999...
9x=9 /:9
x=1

So we create a triangle with two 89.9999... degrees. After infinite distance they should connect and create a triangle, with the third angle equal to 0.0000...1 (It is of course impossible to draw such triangle). But wait, haven't I said before, that 0.999...=1? So 89.9999...=90. So we have triangle with such degrees:
90 (89.999...)
90 (89.999...)
0.00000...1
(This is also a proof that it is possible to create a triangle where the sum of the angles is bigger than 180:
90+90+0.0000...1=180.00000...1 Am I right?)

So either we must say, that it is possible to create a triangle with two 90 degree angles (And therefore triange where angles' sum is larger than 180), or change the rule, and say this:

x=0.99999... /*10
10x=9.99999...0
10x-x=9.99999...0-0.99999...
9x=8.99999...1 /:9
x=0.99999...

Is it true? Hehe...

____________________________
My website | Facebook | Twitter

zex20913
Level: Smitemaster

Rank Points: 1721
Registered: 02-04-2003
IP: Logged

That's why math people say .9999999.....etc =1. Because you get into a lot of such arguments, such as there would be no number between them.

And there would have to be infinitely many 0s before the 1 after your decimal point for that problem.

Silly math.

____________________________

silver
Level: Smitemaster
Rank Points: 915
Registered: 01-18-2005
IP: Logged

"After infinite distance" and "0.00...1" don't exist.

Put another way, nothing happens "after" an infinite count or an infinite distance or an infinite time - because for there to be an "after", there first has to be an ending, and for any infinite series, there is no end.


____________________________

skell
Level: Legendary Smitemaster

Rank Points: 3734
Registered: 12-28-2004
IP: Logged

But it is also even mjore impossible to create something from nothing . So the value smaller than 1 can't give me 1...

____________________________
My website | Facebook | Twitter

Tim
Level: Smitemaster

Rank Points: 1979
Registered: 08-07-2004
IP: Logged

Ahem...

It is even possible to draw a triangle with all three corners having 90 degrees.

skell wrote:
Like somebody mentioend before I recommend all Smullyan's Books.

What? I'm somebody now? I used to have 'To mock a mockingbird' as well, but I've given them away...

____________________________
The best way to lose customers is to let little kids running loose on a forum with too many mod points.

skell
Level: Legendary Smitemaster

Rank Points: 3734
Registered: 12-28-2004
IP: Logged

Tim wrote:
Ahem...

It is even possible to draw a triangle with all three corners having 90 degrees.

Click here to view the secret text

×You have to draw it on a sphere though

Wow. I would like to see it .

Tim wrote:

skell wrote:
Like somebody mentioend before I recommend all Smullyan's Books.

What? I'm somebody now? I used to have 'To mock a mockingbird' as well, but I've given them away...

[offtopic]
Well, yeah, It appears to be that you are somebody. But don't worry. I'm some body. Everyone has some body. The problem comes when you will get *exploded* in Atom bomb's explosion. Then you are nobody. Because you have no body. HAHAHA ! GEt it? HAhahah---... Why *allbodies* are not laughing with me? It's not funny...
[/offtopic]

____________________________
My website | Facebook | Twitter

---

[Last edited by skell at 06-22-2006 09:38 PM]

Briareos
Level: Smitemaster

Rank Points: 3516
Registered: 08-07-2005
IP: Logged

skell wrote:
[offtopic]
Well, yeah, It appears to be that you are somebody. But don't worry. I'm some body. Everyone has some body. The problem comes when you will get *exploded* in Atom bomb's explosion. Then you are nobody. Because you have no body. HAHAHA ! GEt it? HAhahah---... Why *allbodies* are not laughing with me? It's not funny...
[/offtopic]

*snore* Zzzzz...

*snort* Wha...? *looks puzzled, doesn't notice anything out of the ordinary*

*grunt* *goes back to sleep*

np: Galaktlan - Valetajad (Draumar Um Kalt Sumar)

____________________________
"I'm not anti-anything, I'm anti-everything, it fits better." - Sole
R.I.P. Robert Feldhoff (1962-2009)

---

[Last edited by Briareos at 06-22-2006 09:46 PM]

silver
Level: Smitemaster
Rank Points: 915
Registered: 01-18-2005
IP: Logged

skell wrote:

Tim wrote:
Ahem...

It is even possible to draw a triangle with all three corners having 90 degrees.

Click here to view the secret text

×You have to draw it on a sphere though

Wow. I would like to see it .

you have. many times.

take, for example, the image on this page: http://www.mhhe.com/physsci/astronomy/arny/student/webtutor/earth_core/

a triangle formed by the edges of that cut-out has 270 degrees in total (three right angles). it's because in spherical geometry, all triangles have more than 180 degrees ( sum-of-angles (in radians) = pi + area-of-triangle / radius-of-sphere^2 )





____________________________

mrimer
Level: Legendary Smitemaster

Rank Points: 5056
Registered: 02-04-2003
IP: Logged

Has anyone mentioned Sphereland? Engaging extension to Flatland that I recommend.

skell wrote:
So we create a triangle with two 89.9999... degrees. After infinite distance they should connect and create a triangle, with the third angle equal to 0.0000...1

Another way of looking at why this is not possible is because .9999... + .0000...1 does not equal 1. However, .9999...9 + .0000...1 would.

____________________________
Gandalf? Yes... That's what they used to call me.
Gandalf the Grey. That was my name.
I am Gandalf the White.
And I come back to you now at the turn of the tide.

eytanz
Level: Smitemaster

Rank Points: 2708
Registered: 02-05-2003
IP: Logged

mrimer wrote:
Has anyone mentioned Sphereland? Engaging extension to Flatland that I recommend.

skell wrote:
So we create a triangle with two 89.9999... degrees. After infinite distance they should connect and create a triangle, with the third angle equal to 0.0000...1

Another way of looking at why this is not possible is because .9999... + .0000...1 does not equal 1. However, .9999...9 + .0000...1 would.

Assuming a constant value of '...'

Eytan

____________________________
I got my avatar back! Yay!

Syntax
Level: Smitemaster
Rank Points: 1218
Registered: 05-12-2005
IP: Logged

I remember having a book when I was a kid (by Martin Gardner I believe). It was great... picked it up in a 2nd hand book shop (and paid for it). It was basically an extensive collection of those "knights and knaves" (knights *always* tells the truth and knaves *always* lie).

He then goes on to introduce humans, who either do one or the other (but consistently). Even though I guess it's not a "pure" maths book, I'm sure it's something which a DROD player would find as engrossing as myself.

There was also the Island of Bali involved, and something about Pandora's box... all with extensions of the original puzzle theme. Add to that extensive coverage of paradoxes, and autobiographic elements of his amazing life.

Sorry I can't remember the exact title (it was a long time ago), but boy did I love this book!

Tim
Level: Smitemaster

Rank Points: 1979
Registered: 08-07-2004
IP: Logged

Syntax wrote:
Sorry I can't remember the exact title (it was a long time ago), but boy did I love this book!

My dear Syntax, Skell just mentioned it a few posts ago!

Ask your local library for the book called "What is the name of this book?" (by Raymond Smullyan)

It's one of my favourite books.

-- Tim

(By the way, the book is currently out of print, so the only way to get it is going to a library... Oh, and I bought one a long time ago. )

____________________________
The best way to lose customers is to let little kids running loose on a forum with too many mod points.

Syntax
Level: Smitemaster
Rank Points: 1218
Registered: 05-12-2005
IP: Logged

Well, I did read the thread, but the fact I didn't know the title of the book means I was probably taking a risk by posting.

At least I pitched the content slightly more (though I guess I had the wrong author too).

Anyways... I second that! And third! Great, great book...

[EDIT]

And the paperback is available on Amazon... (9 2nd hand copies).

---

[Last edited by Syntax at 06-23-2006 09:34 PM]

jackie1
Level: Roachling
Rank Points: 10
Registered: 05-05-2022
IP: Logged

Thanks for post

____________________________
Hello, i love math and physic