[QUOTE=Richard Cameron]you are quite right: I have both editions of The Book 4104 is not in the 1987/88 edition but it is in the 1997 edition. The three pairs of cube roots are 16 and 2; 15 and 9; and 18 and -12.
[/QUOTE]

Oh, normally taxicabs are calculated only with positive cubes...

[QUOTE=Richard Cameron]

4104: "[B]The smallest integer[/B] that can be represented as the sum of 2 cubes in 3 ways"

[/QUOTE]

If you're talking about "cabtaxi" numbers, the book is wrong!
Cabtaxi(3)=728
6^3 + 8^3
= 9^3 - 1^3
= 12^3 - 10^3
=728

57 is the Heinz number? :innocent:

[QUOTE=fetofs]Oh, normally taxicabs are calculated only with positive cubes...

[/QUOTE]

to be fair, The Book doesn't call the numbers taxicabs or cabtaxis. But...

[QUOTE]If you're talking about "cabtaxi" numbers, the book is wrong!
Cabtaxi(3)=728
6^3 + 8^3
= 9^3 - 1^3
= 12^3 - 10^3
=728
[/QUOTE]

clearly you are right: I will have to check if I have misquoted Wells, or if The Book is wrong!

[QUOTE]57 is the Heinz number? [/QUOTE]

Heinz: "57 varieties". I don't think they put it on the tin any more.

Clutching at straws but:

The smallest orthomagic arrangement of distinct
squares is
4^2 23^2 52^2

32^2 44^2 17^2

47^2 28^2 16^2

and each row and column of this arrangement sums to 3249 = 57^2.

[url="http://www.mathpages.com/home/kmath427.htm"]http://www.mathpages.com/home/kmath427.htm[/url]

I mentioned 57! Do I win some ketchup?

Special whole numbers.
 

[QUOTE=Flatlander]I have the book too! (Since 1988.) I knew Mally was quoting from it so I tried to find numbers that weren't in it :wink:

(Whenever I read a section I find myself saying "Yes, but is it curious or is it interesting?" It's getting really annoying.)

Anyway 1988

or, a bit easier

1888[/QUOTE]
:smile:
OKAY: asfaik you wont find this deduction in any book. After a long search from all sources available I have come up with own version and abs. original
1888:= 888+888+88+8+8+8. Elegant isn't it?
My thanks to Flatlander, Fetofs and Richard Cameron.

Similarly for 1988 which will involve a fraction in 8.
Mally :coffee:

Special whole numbers
 

[QUOTE=Richard Cameron]to be fair, The Book doesn't call the numbers taxicabs or cabtaxis. But...

clearly you are right: I will have to check if I have misquoted Wells, or if The Book is wrong!

Heinz: "57 varieties". I don't think they put it on the tin any more.[/QUOTE]
:rolleyes: Henry Heinz in 1890 actually produced 65 products at the time but he allegedly liked the look of 57.

57: Its the number of letters in the largest official name of a country shortened to LIBYA.

57*C: The highest temp. ever recorded in Azizia. You guessed it, its in Libya.
Source: Adam Spencers 'Book of Numbers' [ Do you have this book Richard?]
Mally :coffee:

Special whole numbers
 

[QUOTE=Flatlander]Clutching at straws but:

The smallest orthomagic arrangement of distinct
squares is
4^2 23^2 52^2

32^2 44^2 17^2

47^2 28^2 16^2

and each row and column of this arrangement sums to 3249 = 57^2.

[url="http://www.mathpages.com/home/kmath427.htm"]http://www.mathpages.com/home/kmath427.htm[/url]

I mentioned 57! Do I win some ketchup?[/QUOTE]

:surprised
57: = 29^2 - 28^2. =3 * 19 (of course this is trivial! )

Thank you Flatlander for the excellent reference to Mathpages and the advanced account on orthomagic squares.

I have the book 'The Zen of magic squares, circles and stars' (2003) by Clifford A Pickover (Ph.D Yale ).
Its a book well reading or acquiring.

He mentions bimagic, trimagic,..p-multimagic (k= 1,2,3... k ) which is much the same but less formidable sounding.
The first quadramagic and pentamagic were created in 2001.

There is a difference though and these are 'superior' to orthomagic squares as even the original unit power square is also magic. He gives examples of these of order 8 and above.
Mally :coffee:

[QUOTE=fetofs]If you're talking about "cabtaxi" numbers, the book is wrong![/QUOTE]

I quoted the book verbatim; so the The Book is indeed wrong. Teach me to quote stuff without checking it first.

on 57, I realised when i posed it that it was likely that people would come up with more interesting features than me. And so it has proved. Very impressive, flatlander.

[QUOTE=mfgoode]57: Its the number of letters in the largest official name of a country shortened to LIBYA.

57*C: The highest temp. ever recorded in Azizia. You guessed it, its in Libya.
Source: Adam Spencers 'Book of Numbers' [ Do you have this book Richard?]
[/QUOTE]

both good, thanks mally. I don't have that book but will look out for it.

Mindful of my comment above about checking stuff, I looked up both extrema.
Russell Ash's "Top Ten Of Everything" had Libya as the longest official country name but gave it as 56 letters. Of course Libya's real official name will be in arabic so I can't really judge. The highest recorded temperature is in the Guinness record book of course. el Azizia 13 september 1922. But its listed as 136.4 F which is 58.0 C. Wikipedia gives it as 135.9 F, 57.7 C ...

I'm yearning for the crystal clarity of mathematics.

Richard

Here's a nice link:

[url="http://www.stetson.edu/~efriedma/numbers.html"]http://www.stetson.edu/~efriedma/numbers.html[/url]

As you proposed many properties on 57, I'll post more numbers:
293
295
297

Note:The site Flatlander posted says that 57=111 in base 9.

[QUOTE=Richard Cameron]I quoted the book verbatim; so the The Book is indeed ...
both good, thanks mally. I don't have that book but will look out for it.

Mindful of my comment above about checking stuff, I looked up both extrema.
Russell Ash's "Top Ten Of Everything" had Libya as the longest official country name but gave it as 56 letters. Of course Libya's real official name will be in arabic so I can't really judge. The highest recorded temperature is in the Guinness record book of course. el Azizia 13 september 1922. But its listed as 136.4 F which is 58.0 C. Wikipedia gives it as 135.9 F, 57.7 C ...

I'm yearning for the crystal clarity of mathematics.

Richard[/QUOTE]
:surprised
Here is the full official name in English which is registered in most of the English speaking countries which I presume is official to the majority.

We must not go checking every trivial fact in a post which are irrelevant to the main stream and this is math facts ,unless you are an editor.When an author publishes his work we expect him to be correct in the facts he presents. There is no necessity to be splitting hairs on non trivial facts or spelling mistakes etc.. We must realise (realize)[another point of contention!] that the m/forum is an international organisation and mistakes in language should be overlooked.

If one wants to excel in a post then make sure your math facts are correct and to hell with spelling mistakes and what have you. There are so many posts where this seems to be the criterion. This leads to flaming and bad blood. IMO this is one upmanship and this should be avoided. If Mersenne bothered about his correspondence with others on such matters we would perhaps have not got the legacy he left behind and so on and so forth.
So here is the official name of Libya.

"Al Jumahiriyah al Arabiyah al Libiyah ash Shabiyah al Ishtirakiyah".

Try not to be petty and attempt to count the letters. The chances are that on the first trial you will get either 56 or 57 or even 58. Is it worth waisting time and proving and saying that 'U have typed it wrong?'

BTW: I checked on Adam Spencer. He states the temp. topped 57*C. A few decimal places here and there doest matter as long as it is higher and not lower than what he states. To include the decimal and to check several seach engines and sites for this In my IMO is being petty minded!
Mally :coffee:

Mally

I prefer 'pedantic' to 'petty' but I think we've had enough of 57: whats the next number?

Richard