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#1551 Re: Dark Discussions at Cafe Infinity » Cow Bull 1 » 2005-12-23 09:21:51
Guess 2: 1973
#1552 Re: Dark Discussions at Cafe Infinity » Can you work in group or who'll be the survivor? » 2005-12-23 09:14:47
For naw everything is OK. Everybody except me have guessed their color right.
#1553 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-12-23 09:10:59
Well done, Ricky!
Your proof is very good.
And I haven't beated you because you was able to give another good proof.
#1554 Re: This is Cool » Trigonometric function with half-square graph? » 2005-12-23 09:06:01
Oops...
Just ArcCos[Sin[x]] makes square.
#1555 Re: This is Cool » Trigonometric function with half-square graph? » 2005-12-23 08:43:51
Sq[x] is periodic with period Pi.
I've started making some pictures.
#1556 Re: This is Cool » Trigonometric function with half-square graph? » 2005-12-23 08:40:56
If ArcCos[Sin[ArcCos[Sin[x]]]] = Sq[x] then I found interesting property:
Sq[Sq[x]]=Sq[x]!
#1557 This is Cool » Trigonometric function with half-square graph? » 2005-12-23 08:38:30
- krassi_holmz
- Replies: 5
This thing is very amasing for me.
t∈[0, π]
x=ArcSin[Cos[t]]
y=ArcCos[Sin[t]]
What is the graphic plot of this parametric sequence?
Yes, this is a square!
And the function
y = ArcCos[Sin[ArcCos[Sin[x]]]]
is half square!
...Interesting...
#1558 Re: Help Me ! » What does this notation mean? » 2005-12-23 08:16:13
Also it may be something from the group theory, I guess.
#1559 Re: Help Me ! » Another Question Via Email » 2005-12-23 08:14:03
And for my problem:I prooved that ther there isn't third number. That means that for number k greater than 6 there exist prime number p that is not from the form ik +- 1.
#1560 Re: Help Me ! » Very interesting problems.. » 2005-12-23 07:51:07
And for the Ricky's suggest that √2 is not even rational. Here's interesting theorem:
Let Q is the multitude of all numbers of the type a/b , a,b ∈ N (naturals)
Let R is the multitude of all numbers of the type a√b (b^(1/a)) , a,b ∈ N (naturals)
Then Q && R = N.
That means that every a√b that is not natural is not rational and every a/b that is not natural is not a root of an integer number.
#1561 Re: Help Me ! » Very interesting problems.. » 2005-12-23 07:42:19
The the remainder of the sum of every two consecutive numbers when it's divided by 4 must be 0 or 1.
#1562 Re: Help Me ! » Very interesting problems.. » 2005-12-23 07:21:23
Here are some analisys that may be helpful:
We have n numbers between 1 and n. Their sum is n(n+1)/2.
Every two consecutive numbers make a perfect square. The sum of all perfect squares is 2n(n+1)/2=n(n+1)
so n(n+1) must be sum of n squares greater than 1.
#1563 Re: Help Me ! » lg problem » 2005-12-23 06:54:18
2^10000 = 199506311688075838488374216268358508382349683188619245485200894985294388302219\
466319199616840361945978993311294232091242715564913494137811175937859320963239\
578557300467937945267652465512660598955205500869181933115425086084606181046855\
090748660896248880904898948380092539416332578506215683094739025569123880652250\
966438744410467598716269854532228685381616943157756296407628368807607322285350\
916414761839563814589694638994108409605362678210646214273333940365255656495306\
031426802349694003359343166514592977732796657756061725820314079941981796073782\
456837622800373028854872519008344645814546505579296014148339216157345881392570\
953797691192778008269577356744441230620187578363255027283237892707103738028663\
930314281332414016241956716905740614196543423246388012488561473052074319922596\
117962501309928602417083408076059323201612684922884962558413128440615367389514\
871142563151110897455142033138202029316409575964647560104058458415660720449628\
670165150619206310041864222759086709005746064178569519114560550682512504060075\
198422618980592371180544447880729063952425483392219827074044731623767608466130\
337787060398034131971334936546227005631699374555082417809728109832913144035718\
775247685098572769379264332215993998768866608083688378380276432827751722736575\
727447841122943897338108616074232532919748131201976041782819656974758981645312\
584341359598627841301281854062834766490886905210475808826158239619857701224070\
443305830758690393196046034049731565832086721059133009037528234155397453943977\
152574552905102123109473216107534748257407752739863482984983407569379556466386\
218745694992790165721037013644331358172143117913982229838458473344402709641828\
510050729277483645505786345011008529878123894739286995408343461588070439591189\
858151457791771436196987281314594837832020814749821718580113890712282509058268\
174362205774759214176537156877256149045829049924610286300815355833081301019876\
758562343435389554091756234008448875261626435686488335194637203772932400944562\
469232543504006780272738377553764067268986362410374914109667185570507590981002\
467898801782719259533812824219540283027594084489550146766683896979968862416363\
133763939033734558014076367418777110553842257394991101864682196965816514851304\
942223699477147630691554682176828762003627772577237813653316111968112807926694\
818872012986436607685516398605346022978715575179473852463694469230878942659482\
170080511203223654962881690357391213683383935917564187338505109702716139154395\
909915981546544173363116569360311222499379699992267817323580231118626445752991\
357581750081998392362846152498810889602322443621737716180863570154684840586223\
297928538756234865564405369626220189635710288123615675125433383032700290976686\
505685571575055167275188991941297113376901499161813151715440077286505731895574\
509203301853048471138183154073240533190384620840364217637039115506397890007428\
536721962809034779745333204683687958685802379522186291200807428195513179481576\
244482985184615097048880272747215746881315947504097321150804981904558034168269\
49787141316063210686391511681774304792596709376. It has exactly 3011 digits.
#1564 Re: Help Me ! » Very interesting problems.. » 2005-12-23 06:48:53
what means that the sum is perfect square?
#1565 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-12-23 06:29:40
#1566 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-12-23 06:23:51
Here's plot of the function Prime[i+1]-Prime[i] up to 1000.
Actually, it's Prime[Floor[i+1]]-Prime[Floor[i]]
#1567 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-12-23 06:15:38
#1568 Re: Guestbook » 16 Year Old Winning Big Award » 2005-12-18 19:25:11
What he actually did was a nice theory about Riemann maps and Bergman kernels!
#1569 Re: Introductions » Hi » 2005-12-18 19:16:46
That means Hi.
#1570 Re: Introductions » Здрасти by krassi_holmz » 2005-12-18 19:12:40
Chaotic is absolutely right!
#1571 Re: Introductions » Hello Maths Whizzes » 2005-12-18 19:10:02
Why? PunBB is not sssssssso bad.
#1572 Re: Introductions » Glad to be here! » 2005-12-18 19:06:19
Hello.
And here is the place were you can get all the help you need.
#1573 Re: Help Me ! » Limits and multiple variables » 2005-12-18 18:20:35
#1574 Re: Help Me ! » Limits and multiple variables » 2005-12-18 18:19:03
But it won't work in all ways: It can bring to something like that:
#1575 Re: Help Me ! » Limits and multiple variables » 2005-12-18 18:17:11
If you are able to reduce your limit to sum of non-multiple limits you can find them and then you can sumarize them.