Favourite 10 Numbers Under 100

[jkmccrann]

Having just read another thread, thought I mnight ask here. Can anyone who reads this thread pick their favourite 10 (or 5 or 20, whatever you feel like) numbers Under 100?

To get things started, mine are
17, 7, 37, 79, 47, 23, 49, 97, 73, 19.

Does anyone else exhibit such a pronounced bias as I do?

Cheers

[Hugh Jass]

I'd be willing to bet most folks do. I generally lean toward 2s and 8s.

22, 2, 8, 10, 34, 44, 88, 48, Does 00 count?

[cjl]

11, 1, 55, 86, 98, 28, 13, 6, 73, 2

[Egarim]

7,11,12,15,24,32,45...meh thats it.

24 is my favorite. Wore that one when playing baseball from age 13-19.

[Heid the Ba']

15, 19, 28, 30, 42, 44, 45, 72, 74, 90

[kashi]

26 is my favourite. It's the only number in all infinity to be wedged directly in between a perfect square (25) and a perfect cube (27).

[Swift]

My favorite 10 numbers under 100 are 11 and 10.
Oh, I'm sorry, I thought we were talking in binary! :o

[turbo-1]

Just one...pi

[zebo-the-fat]

69 :o

[Grey]

26 is my favourite. It's the only number in all infinity to be wedged directly in between a perfect square (25) and a perfect cube (27).Hmm. It looks that way for small values, but do you actually know of a proof of that? There's at least a degenerate case (0, wedged between 1^2 and -1^3), but we can probably ignore that one. Now I'm curious.

[TheBlackCat]

13, 31, 2, and i. 13 because many other people don't like it, 31 because it is 13 backwards, and 2 because it is the only number where it gives the same answer if you add it to itself, multiply it byself, or raise it to its own power. It is also the only even prime number, the smallest positive prime number, and probably one of the most-used numbers in math (doubling something, halving something, squaring something, and square rooting something are all extremely common operations, and raising 2 to some power is another very common operation). It is also the base of binary numbers, and its multiples are the bases in octal and hexadicaml numbers. Most animals on Earth are bilaterally symmetrical, and most things we experience are either dualistic, paired, or a continuum between two extremes. i is just fun, and it is technically lower than 100 on a real/imaginary 2D plot (since it lies on the real=0 line) so I will include it.

[The Supreme Canuck]

8. And for some reason I prefer even numbers to odd. Weird, eh?

[TheBlackCat]

Hmm. It looks that way for small values, but do you actually know of a proof of that? There's at least a degenerate case (0, wedged between 1^2 and -1^3), but we can probably ignore that one. Now I'm curious.

-25 is wedged between (5i)^2 and (-3)^3

[tlbs101]

Any 10 numbers that will produce a winning Keno ticket, are my favorites :D .

[Nicolas]

69 :o

I do like the number 69 because of its symmetry. I like the number 88 as well as it fills up your calculator :).

I am one of those persons who sometimes types a "p" when there should be a 9. Nevertheless, I like things with a 9. The "almost" numbers :).

[pumpkinpie]

13, 31, 2, and i. 13 because many other people don't like it, 31 because it is 13 backwards, and 2 because it is the only number where it gives the same answer if you add it to itself, multiply it byself, or raise it to its own power. It is also the only even prime number, the smallest positive prime number, and probably one of the most-used numbers in math (doubling something, halving something, squaring something, and square rooting something are all extremely common operations, and raising 2 to some power is another very common operation). It is also the base of binary numbers, and its multiples are the bases in octal and hexadicaml numbers. Most animals on Earth are bilaterally symmetrical, and most things we experience are either dualistic, paired, or a continuum between two extremes. i is just fun, and it is technically lower than 100 on a real/imaginary 2D plot (since it lies on the real=0 line) so I will include it.

Wow, that #2 is such a lucky duck!

Here's my list....3,24,33,76....I guess those are the only ones that mean anything to me. Maybe pi and e too.

[Grey]

-25 is wedged between (5i)^2 and (-3)^3I assume you meant -26. Quite correct. If I can extend things to the realm of negative numbers, why not complex ones as well. :) Still, I'm curious about my original question. Are there any other examples (within the positive integers, let us say) of a perfect square and a perfect cube that differ by exactly two? Or conversely, can anyone show a proof that there are no such cases? This made me think of a vaguely comparable case, the spacing of the prime numbers. Although the average separation of adjacent prime numbers increases without bound as one looks at the sequence of primes, one can also show that there are infinitely many pairs of primes separated by two.

[Swift]

In base 10, my two favorites are:
73.59025701235780123423097230970128347827359872398 4786187239847
and 4
;)

[Dragon Star]

I like 5, as for an explanation, I don't have one...

[LurchGS]

36
24
34
69
66
2


That's all I can think of... just a set of .. of... totally random numbers, yeah.. yeah, that's the ticket!

[Matherly]

(Matherly starts muttering)

5 8 15 16 23 42...

(for an explination, see here (http://en.wikipedia.org/wiki/Lost_%28TV_series%29#Numbers))

[LurchGS]

wwwwwwaaaaaaaaayyy too much bad TV in your life

[aurora]

11
12
14
15
16
17

For obvious reasons.

Oh, and 42, for a different obvious reason.

[ZaphodBeeblebrox]

1, 4, 9, 16, 25, 36, 49, 64, 81

Or Maybe:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91

I Think, It's Pretty Much, Self-Explanatory!!!!

[Andromeda321]

5 is my favorite number because when I was five years old I decided it would forever be my favorite number. I was pretty bummed when I turned 6 though, so that is hence my second favorite number. :)
I also am wary of prime numbers for some reason. I mean those guys don't want to play nice with all the little ones so you can't quite trust 'em!

[ZaphodBeeblebrox]

I'd be willing to bet most folks do. I generally lean toward 2s and 8s.

22, 2, 8, 10, 34, 44, 88, 48, Does 00 count?
Only On, an American Roulette Wheel!!!!

:wall:

:think:

[Hugh Jass]

Can't believe I forgot 11, aka about 11! for too many reasons I can list, should have been at the top of my list.

[Maksutov]

In semi-particular order:

6, 66, 0, 1, 1.414213562, 2.718281828..., 9, 10, 13, 99.74

Runners-up:

2.5029078750, 4.6692016091, 0.628, 2, 3

[TheBlackCat]

I assume you meant -26. Quite correct. If I can extend things to the realm of negative numbers, why not complex ones as well. :) Still, I'm curious about my original question. Are there any other examples (within the positive integers, let us say) of a perfect square and a perfect cube that differ by exactly two? Or conversely, can anyone show a proof that there are no such cases? This made me think of a vaguely comparable case, the spacing of the prime numbers. Although the average separation of adjacent prime numbers increases without bound as one looks at the sequence of primes, one can also show that there are infinitely many pairs of primes separated by two.

Well, lets see. Such a number would meet the requirement of

y^2=x^3+2 or y^2=x^3-2

Or y=sqrt(x^3+{1,-1}*2)

However, I do not know how to solve this problem analytically for integers. So I made a calculator program to do it automatically by brute force. After going through the first 1000 x values with no luck I gave up.

[rahuldandekar]

19, 13, e, 25.

19 is my favourite (I dunno why :confused: ) And 13 is lucky for me (no, I'm not Satan ;) ) .

[jkmccrann]

In semi-particular order:

6, 66, 0, 1, 1.414213562, 2.718281828..., 9, 10, 13, 99.74

Runners-up:

2.5029078750, 4.6692016091, 0.628, 2, 3

99.74? You'll have to explain that one to me, or is that the boiling point of water in Centrigrade?

Thinking along this again, I do have to admit a liking for e & pi.

Thanks for responses guys, very interesting to see everything you've come up with.

[kashi]

Hmm. It looks that way for small values, but do you actually know of a proof of that? There's at least a degenerate case (0, wedged between 1^2 and -1^3), but we can probably ignore that one. Now I'm curious.

I shall correct my previous statement:

26 is the only integer wedged between a positive perfect square and a positive perfect cube. I have heard a mathematician talk about this on radio but I have not seen the proof with my own eyes.

Here's a page which lists special properties for some integers up to 9999:

http://www.stetson.edu/~efriedma/numbers.html

[paulie jay]

When I was 7 I picked the winning horses in a trifecta - 2,16 and 8. My dad put the bet on and I won $320 - in 1977!



For some reason I've always had a thing for the number 37.

[pumpkinpie]

(Matherly starts muttering)

5 8 15 16 23 42...

(for an explination, see here (http://en.wikipedia.org/wiki/Lost_%28TV_series%29#Numbers))


I was going to post that....but I wasn't sure of the numbers and didn't feel like looking them up! :lol:

And LurchGS, it's NOT bad tv at all---some of the best tv I've ever watched! In my opinion. Is that your opinion having watched it yourself?

[kashi]

OH pllleeeaasee. Terrible, terrible show.

[pumpkinpie]

I can respect the fact that you and others don't care for it, but I take offense to the "what a horrible show--why on earth would anyone watch it? I think it's terrible so no one should like it." type of comment. I enjoy it, that's why I like it! Please don't try to make me look stupid for liking it.

[Grey]

26 is the only integer wedged between a positive perfect square and a positive perfect cube. I have heard a mathematician talk about this on radio but I have not seen the proof with my own eyes.Now I really want to track down an actual proof. :neutral:

Here's a page which lists special properties for some integers up to 9999:That's a great list!

[mickal555]

Ummm...

I like...

42! (meaning of liff)

and...

13! (to snubb my nose at suspisiouse people)

7 (the length of my first middle and surnames)

3.141592653589793238462643383279502884197169399375 10582097494459230781640628620899862803482534211706 79821480865132823066470938446095505822317253594081 28481117450284102701938521105559644622948954930381 96442881097566593344612847564823378678316527120190 91456485669234603486104543266482133936072602491412 73724587006606315588174881520920962829254091715364 36789259036001133053054882046652138414695194151160 94330572703657595919530921861173819326117931051185 48074462379962749567351885752724891227938183011949 12983367336244065664308602139494639522473719070217 98609437027705392171762931767523846748184676694051 32000568127145263560827785771342757789609173637178 72146844090122495343014654958537105079227968925892 35420199561121290219608640344181598136297747713099 60518707211349999998372978049951059731732816096318 59502445945534690830264252230825334468503526193118 81710100031378387528865875332083814206171776691473 03598253490428755468731159562863882353787593751957 78185778053217122680661300192787661119590921642019 89380952572010654858632788659361533818279682303019 52035301852968995773622599413891249721775283479131 51557485724245415069595082953311686172785588907509 83817546374649393192550604009277016711390098488240 12858361603563707660104710181942955596198946767837 44944825537977472684710404753464620804668425906949 12933136770289891521047521620569660240580381501935 11253382430035587640247496473263914199272604269922 79678235478163600934172164121992458631503028618297 45557067498385054945885869269956909272107975093029 55321165344987202755960236480665499119881834797753 56636980742654252786255181841757467289097777279380 00816470600161452491921732172147723501414419735685 48161361157352552133475741849468438523323907394143 33454776241686251898356948556209921922218427255025 42568876717904946016534668049886272327917860857843 83827967976681454100953883786360950680064225125205 11739298489608412848862694560424196528502221066118 63067442786220391949450471237137869609563643719172 87467764657573962413890865832645995813390478027590 09946576407895126946839835259570982582262052248940 77267194782684826014769909026401363944374553050682 03496252451749399651431429809190659250937221696461 51570985838741059788595977297549893016175392846813 82686838689427741559918559252459539594310499725246 80845987273644695848653836736222626099124608051243 88439045124413654976278079771569143599770012961608 94416948685558484063534220722258284886481584560285 06016842739452267467678895252138522549954666727823 98645659611635488623057745649803559363456817432411 25150760694794510965960940252288797108931456691368 67228748940560101503308617928680920874760917824938 58900971490967598526136554978189312978482168299894 87226588048575640142704775551323796414515237462343 64542858444795265867821051141354735739523113427166 10213596953623144295248493718711014576540359027993 44037420073105785390621983874478084784896833214457 13868751943506430218453191048481005370614680674919 27819119793995206141966342875444064374512371819217 99983910159195618146751426912397489409071864942319 61567945208095146550225231603881930142093762137855 95663893778708303906979207734672218256259966150142
and...

69, 10, 16, 0, 26, 18

[Grey]

A Google search turned up this (http://www.trottermath.net/numtrivia/specnum2.html) page, which says that there's a proof by Euler from 200 years ago that 26 is the only number one larger than a square and one smaller than a cube. Further searaching gives us this (http://www.trottermath.net/probsolv/sqcube.html) page, which gives an actual proof. This may leave open the question of whether there is a number one larger than a cube and one smaller than a square (which would still therefore be "wedged between" them). I'll see if the proof given can be modified to cover that case as well.

[TheBlackCat]

I couldn't find such a number.

[Dragon Star]

<snip>

Dude, is that number real? I mean, did they actually get that far with Pi?

[Wolverine]

Pi to 1,000,000 places (http://3.141592653589793238462643383279502884197169399375 105820974944592.com/)...

[Dragon Star]

Pi to 1,000,000 places (http://3.141592653589793238462643383279502884197169399375 105820974944592.com/)...


O_oI think my head just blew up....*twitch*

As soon as I saw the pic of Dr. Evil I started cracking up...

[hippietrekx]

I quite like -216. You know, -6^3? or -6 x -6 x -6? :D

And 2. Not sure why. :confused:

Let us not forget 29 and 36 along with -1.

And I kinda like 87 as well. *shrug*

--hipster

[montebianco]

So, mickal555, one of your favorites is a number which is really, really close to pi? :D

TheBlackCat, how is i less than 100? Its modulus is less than 100, if that's what you mean. Certainly its real part is smaller than the real part of 100, but then its imaginary part is greater than the imaginary part of 100...

Hipster, -216 is indeed less than 100 :D - BTW, new word puzzle posted at Scotson's Shack

[TheBlackCat]

TheBlackCat, how is i less than 100? Its modulus is less than 100, if that's what you mean. Certainly its real part is smaller than the real part of 100, but then its imaginary part is greater than the imaginary part of 100...

It depends on how you define "less than 100". In a traditional number line, with larger numbers to the right and lower numbers to the left, everything to the left of 100 is defined as "less than 100". If you expand the tradional number line to include complex numbers, you get a plane. But if you use the same rule where everything to th left of 100 is less than 100, i.e. anything to the left of the real=100 line, i would be less than 100. However, if you start with the imaginary number line and expand it to include the real number line, then you would get the opposite result. Since there is a definition of "less than" that includes i being less than 100, then it is valid to say i is less than 100. That does not mean i is also not greater than 100, less than and greater than on a plane (or a volume for that matter) depends on how you define it.

[TheBlackCat]

Pi to 1,000,000 places (http://3.141592653589793238462643383279502884197169399375 105820974944592.com/)...

Bah, that's nothing: Pi to 30,000,000 decimal places (http://oldweb.cecm.sfu.ca/projects/ISC/data/pi.html)
And if that's not enough: Pi to 400,000,000 decimal place (http://highpi.4t.com/custom.html)
I know there was a distributed computing project called PiHex that got to the 1 Quadrillionth binary digit of pi

Edit: Assuming my calculations are correct, that last one should be a little over the 301 trillionth decimal digit of pi

[montebianco]

It depends on how you define "less than 100". In a traditional number line, with larger numbers to the right and lower numbers to the left, everything to the left of 100 is defined as "less than 100". If you expand the tradional number line to include complex numbers, you get a plane. But if you use the same rule where everything to th left of 100 is less than 100, i.e. anything to the left of the real=100 line, i would be less than 100. However, if you start with the imaginary number line and expand it to include the real number line, then you would get the opposite result. Since there is a definition of "less than" that includes i being less than 100, then it is valid to say i is less than 100. That does not mean i is also not greater than 100, less than and greater than on a plane (or a volume for that matter) depends on how you define it.

Well, I agree that's what you get, but I have never seen anyone define a "less than" relationship by X<Y as (real part of X)<(real part of Y) :D

[mickal555]

Pi to 1,000,000 places (http://3.141592653589793238462643383279502884197169399375 105820974944592.com/)...

heh heh heh :D:lol:

Bah, that's nothing: Pi to 30,000,000 decimal places (http://oldweb.cecm.sfu.ca/projects/ISC/data/pi.html)
And if that's not enough: Pi to 400,000,000 decimal place (http://highpi.4t.com/custom.html)
I know there was a distributed computing project called PiHex that got to the 1 Quadrillionth binary digit of pi

Edit: Assuming my calculations are correct, that last one should be a little over the 301 trillionth decimal digit of pi

:D :D
awesome- I'm gonna download some of them

[Dragon Star]

Wow, it seems that the Pi record is 1.24 trillion decimal places, and was set in 2002, check it out Here (http://www.pen.k12.va.us/Div/Winchester/jhhs/math/facts/pifacts3.html)

[mugaliens]

0, 1, 7, 12, 13, 26, 40, 60, 66, 99

0 and 1 are binary

7, 12, 40, are symbolic

13 tempts fait

26 for what kashi said

60 for it's basis in navigation and time throughout history

66 for the infamous road

99 because Smart never deserved such a good-looking intelligent co-agent

[Nicolas]

Wow, it seems that the Pi record is 1.24 trillion decimal places, and was set in 2002, check it out Here (http://www.pen.k12.va.us/Div/Winchester/jhhs/math/facts/pifacts3.html)

Those records have lost some of their value since the Bailey-Borwein-Plouffe algorithm which can calculate any digit of PI without knowing the preceding digits, be it in a hexadecimal scale.

[Dragon Star]

Those records have lost some of their value since the Bailey-Borwein-Plouffe algorithm which can calculate any digit of PI without knowing the preceding digits, be it in a hexadecimal scale.

How is this, I thought there were no patterns in Pi?

[jkmccrann]

It depends on how you define "less than 100". In a traditional number line, with larger numbers to the right and lower numbers to the left, everything to the left of 100 is defined as "less than 100". If you expand the tradional number line to include complex numbers, you get a plane. But if you use the same rule where everything to th left of 100 is less than 100, i.e. anything to the left of the real=100 line, i would be less than 100. However, if you start with the imaginary number line and expand it to include the real number line, then you would get the opposite result. Since there is a definition of "less than" that includes i being less than 100, then it is valid to say i is less than 100. That does not mean i is also not greater than 100, less than and greater than on a plane (or a volume for that matter) depends on how you define it.

I accept your argument for complex numbers! Remember doing a few weeks on them in high school, but that was the last time I came across i! Always loved how i*i = -1.

No problems here. I haven't done anything remotely resembling Mathematical study for probably 7 years now, which is why I always forget these things when I post topics in here and don't go to the trouble of fully defining a topic! I, bytheway, absolutely fully endorse exploiting the wording of a topic and stretching it as much as possible.

[montebianco]

I accept your argument for complex numbers! Remember doing a few weeks on them in high school, but that was the last time I came across i! Always loved how i*i = -1.

No problems here. I haven't done anything remotely resembling Mathematical study for probably 7 years now, which is why I always forget these things when I post topics in here and don't go to the trouble of fully defining a topic! I, bytheway, absolutely fully endorse exploiting the wording of a topic and stretching it as much as possible.

We usually don't impose an ordering on the complex numbers, the way we do on the real numbers. But, by the method specified, I can claim that (10^1,000,000,000,000)-(10^(-1,000,000,000))*i is less than 100 if I rotate the axes...

[Grey]

We usually don't impose an ordering on the complex numbers, the way we do on the real numbers.Because we can't! That is, for the real numbers it's possible to define an order so that, for any two numbers which are not the same, one will be unambiguously smaller than the other. It's not actually possible to do that with the complex numbers.

[ZaphodBeeblebrox]

I accept your argument for complex numbers! Remember doing a few weeks on them in high school, but that was the last time I came across i! Always loved how i*i = -1.
The BEST Part ...

Is How i^1 = i, i^2 = -1, i^3 = -i, and i^4 = 1!

And Then, It Repeats!!!

:eek:

[Nicolas]

How is this, I thought there were no patterns in Pi?

I don't know the details. There are no patterns, but there is of course the definition of what PI is. Apparently, that allows to calculate a digit without knowing the preceding digits. That doesn't mean there needs to be a repeating pattern however. You could call it a pattern with zero repeat if you like :).

You'd have to look up the details as I don't know them.

[montebianco]

Because we can't! That is, for the real numbers it's possible to define an order so that, for any two numbers which are not the same, one will be unambiguously smaller than the other. It's not actually possible to do that with the complex numbers.

Well, I can define x < y if Re(x)<Re(y) or if Re(x)=Re(y) and Im(x)<Im(y) :D
But this won't have the properties we would normally expect from an ordering...

[GDwarf]

Let's see... 3.141592654 (From memory, wheee), 6.283185308 (Radians to a circle),
8, 16, 32, 64 (useful for calculating sizes for computer hardware.),
88,
50 (Always the first guess in a Hi-Lo game),
25,
24 (% of words that are made up in the poem Jabberwocky).

[turbo-1]

O frabjous day!