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#3551 Help Me ! » Physics motion question » 2005-08-30 14:13:37

John E. Franklin
Replies: 0

Years ago, I saw this problem done out on a chalkboard.  If a small frictionless object is placed on
the top of a sphere or dome, and the object begins to slide down in any direction.  Where does the
small object fly off of the sphere or dome.  You can assume no air friction, no rotational momentum,
no surface tension, etc.  I don't really need this solved but am just interested what you think.  tongue

#3552 Re: This is Cool » Remembering sin and cos values » 2005-08-30 13:33:53

I associate cosine with the x-axis so cosine it is positive in 1st and 4th quadrants.
I associate sine with the y-axis so it is positive in the 1st and 2nd quadrants.
Since tangent is rise over run, or slope, or the derivative of a curve (the tangent of the curve),
then the tangent is positive in 1st and 3rd quadrants.

#3553 Re: Help Me ! » Converting 3.14159265358979323846 into base-26 using alphabet » 2005-08-30 13:01:53

I have been noticing something logarithmic that someone taught me years ago.
The number of digits in the base-26 number to be similar accuracy as the base-10 number
is approximately the length of the base-10 number divided by the common log of 26.
In other words, the base-26 number is shorter in digits by a factor of log(26) or 1.41.
My latest run of the program ran slower because the whole numbers were over 2400
digits long.  I haven't read the documentation of Just BASIC enough to know what the
limit is, but I am happy it seems to be working.  Here is pi in base-26 to over 1700 digits.

pi in base-26 where Z=0, A=1, B=2, C=3, ... X=24, Y=25.

C.
CQRPKNKXQSQNC
MKGMPSFJTCPFS
THQWMDPABJARY
HUPPUFCLDKLTD
WQNHPHXZKUTYU
DALHIOPPWKJOK
QMBEVIOAXLFFN
GILLPHRLRRBHD
JGUCTSBWSIORA
VGTENLPIZNRXF
ONVTOXLKHEREH
HYQNCOKXWODCN
RWLEPSPGLEWEO
UYDYQJEBVJWGS
GTGBOKDLKMTCS
LROVAAIEFRIGM
BNWYMCFGJUNYQ
MJVACLETZXIEN
YWXCJZXLMPTVK
XJZOKXAHYTXAQ
NTIYMCCILNIXN
YRBJRVOJOZCXK
OBSKICHKJTTVJ
PJVIJSYLDKFBN
GQAQIDMQPUGIS
GCKDDIUHEZEPH
BPRLSIEOOYWYN
GXPKVDCECPIQM
TGQKLBMJVPIOZ
LUMNSFUXIPMYL
TBTLXUMCAOFLY
UZLKTEAQYZOLT
JSRJATOEZUKRV
SVLZDSLUDCBHT
ISWLJMUWJCSEF
EGPAZMJNQMOEA
FMBCTJVYOJKSN
ADLNBNIFFWXAU
NZDSLGBSSLZIC
WZTVVOXULTERT
CIUNBLZGLHHGM
BKXVMOHNIDFPV
YLVQTXPDVIXUA
TGNNVZLBSTWQH
HHQURKKSZUTSV
AFWLDFFEIVPLR
UMWHODZYKACKM
GRWYDCPPCNKZO
DYGJVLNZDQKRT
IWUUGJQEJEDYO
BGKLOCVQUDQNB
JVGOPECNVNXUI
VOWTNFXGSHCTZ
QPYGDPPUNMKLU
YRMNOZWMKDJEM
DVEBDTIKDWUDC
LMLGTXNWEZMTI
BELURXMVSTGOV
KPPFMUQANBIGW
DHUKNXWWXVUZR
YGORDOMKVDYFR
NVODVVURUXSSS
WKRVBVBDGDGBV
CELWMLLGPRTUX
HXVIKFGHIBKGX
YSRAJOKGJPMBC
UQVQRHAJRZNHS
USZWMCXJMGLLQ
OUHIXIKWMGPST
YPPBSBJCKCVAQ
APYLUFUGTAYDE
JGRKCHLEKQOZC
MSIABBCTHKNHJ
ILPEAUECDPNDN
RMWQECLKNOBRQ
DIESFQPDAOOXK
THXRKAANEMXYP
XMQLYYSDGCXTP
XQMYWHRJBCCSA
SKVFWXGLRZEAK
ASWMHQNPLJTJT
SUDOMPWMUYYVS
XLYEBOURQXFBX
FRUPTERACZQTT
VIHPVNHXHICFV
TZPKVIRPVGHHY
NZGTRCKBLETTK
HJTPOGVQTTKDL
OBUNCOBVXYQCI
HYHLYTYCEIYZZ
KIRIQUCNVGLBI
CQLJURMGFFLRC
AEBKMBPGGSCZM
QFFPKBFSHGJEP
GWYCFLCRKONWR
HVLCFROEBXXKQ
DKDKKFMYPJPHR
IGGTYHDUVTYUK
XLWGCNOBHKEQK
DAUIXQNQGGGJF
VYZRRVCACQLKQ
WOCEPPBJJNHPS
RYNRMXWQRHMPI
GTWMZQSHCJBEZ
QBJBOZZPZBERO
IWNOZFJTQQRYA
JPINCLZSXIMZB
DSUVXKYBVFLIV
LDTFRSKACJOWL
VMWHKGDGSEEMM
UXLENEISPQTUT
OLJDRSWZPHIXH
JOWGZNALVKHCW
DCGCQCDCSCPHE
EVWNQRZYAXHKB
WCVBNPJXAJBVS
JKOEEHFIAJASW
ODJVMDTCNIOLP
WAMRFXYRJDDBR
DYZKGQVENKHYM
FVVQNZSMZLCQI
SXFHAVAOXPFGX
NIIWVUESTQFFT
WKICWRZDFGRNB
DRRSTJMGMWSPU
GWWRCCUFFZSKJ
ZDGYPLZILDFJU
EJDRFLQXMFHZM
VSIZATHPVHKTK
UTVSCQSGAVIBC
IIZJFCSAMMHDI
MGVQODXTJNIEU
IUJFGK
Started with a base-10 accuracy of 2438 decimal places.
# of digits found is: 1722

smile

#3554 Re: Help Me ! » Converting 3.14159265358979323846 into base-26 using alphabet » 2005-08-30 10:22:09

That would be cool to find words in pi!  Here are the results a little neater:

pi in base-26 where Z=0, A=1, B=2, C=3, ... X=24, Y=25.

C.
CQRPKNKXQSQNC
MKGMPSFJTCPFS
THQWMDPABJARY
HUPPUFCLDKLTD
WQNHPHXZKUTYU
DALHIOPPWKJOK
QMBEVIOAXLFFN
GILLPHRLRRBHD
JGUCTSBWSIORA
VGTENLPIZNRXF
ONVTOXLKHE

#3555 Re: Help Me ! » Converting 3.14159265358979323846 into base-26 using alphabet » 2005-08-30 09:07:56

Hi again...

The BASIC program was a preliminary version.  I added these lines so the letter Z could be displayed not as an @ (at sign).  The @ sign precedes the capital letters in the ASCII chart, #64.
   if "@"= nextMinChar$ then nextMinChar$= "Z"
   if "@"= nextMaxChar$ then nextMaxChar$= "Z"
Also the loopAround number of times I changed as needed for different tests.
Also the last and longest one that min and max digits diverge at the 140th decimal place in base-26, that run of the program started off with 199 decimal places of pi in base-10.  I noticed it went off the screen to the right and couldn't be viewed even with
the horizontal scroll bar.  Anyway, it was kind of messy above, but I didn't want to edit the file or I might have accidentally deleted the correct data.  Finally, the left column is the minimum possible digit, and the right column is the maximum possible digit value.

#3556 Re: Help Me ! » Converting 3.14159265358979323846 into base-26 using alphabet » 2005-08-30 08:13:42

I wrote a "Just BASIC" program to compute the digits.  I used a max and min value for pi so I could see where the results diverged.  See results below.

C.CQRPK

piMax in decimal started out as: 14159265358979323847, This is: 20 digits.
piMin in decimal started out as: 14159265358979323846, This is: 20 digits.
(C,C)
(Q,Q)
(R,R)
(P,P)
(K,K)
(N,N)
(K,K)
(X,X)
(Q,Q)
(S,S)
(Q,Q)
(N,N)
(C,C)
(M,M)    fourteen digits!   Tuesday, August 30, 2005  
(F,W) This is where min and max diverge.
(V,P)
(F,H)
(M,T)
(B,E)
(L,C)
(U,T)
(Q,J)
(I,Y)
(F,F)
(R,V)
________________________________________
see code below by John E. Franklin...
'program name: base26pi_BBK.bas  (using Just BASIC v1.0 from internet)
piMax= 14159265358979323847''6'264338327950288419716939937511
piMin= 14159265358979323846   '264338327950288419716939937510
piMaxString$= STR$(piMax)
piMinString$= STR$(piMin)
piMaxLen= LEN(piMaxString$)
piMinLen= LEN(piMinString$)

print "piMax in decimal started out as: ";piMax;", This is: ";piMaxLen;" digits."
print "piMin in decimal started out as: ";piMin;", This is: ";piMinLen;" digits."

nextMax= piMax
nextMin= piMin

'commence loop
For loopAround= 1 to 25
nextMax= nextMax * 26
nextMin= nextMin * 26
nextMaxString$= STR$(nextMax)
nextMinString$= STR$(nextMin)
rightMaxString$= RIGHT$(nextMaxString$,piMaxLen)
rightMinString$= RIGHT$(nextMinString$,piMinLen)
leftMaxString$= LEFT$(nextMaxString$,LEN(nextMaxString$) - piMaxLen)
leftMinString$= LEFT$(nextMinString$,LEN(nextMinString$) - piMinLen)
'print "@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@"
'print leftMaxString$;"%";rightMaxString$
'print leftMinString$;"%";rightMinString$
leftMax= val(leftMaxString$)
leftMin= val(leftMinString$)
'print "Next Max Digit is: ";CHR$(leftMax + 64);" ";leftMax
'print "Next Min Digit is: ";CHR$(leftMin + 64);" ";leftMin
nextMaxChar$=CHR$(leftMax + 64)
nextMinChar$=CHR$(leftMin + 64)
print "(";nextMinChar$;",";nextMaxChar$;")"

nextMax= val(rightMaxString$)
nextMin= val(rightMinString$)

next loopAround
_______________________________________________________
piMax in decimal started out as: 14160, This is: 5 digits.
piMin in decimal started out as: 14159, This is: 5 digits.
(C,C)
(Q,Q)
(R,R)
(O,S)  Diverges after 3rd digit.
(F,T)
(Z,U)
(R,V)
_______________________________________________
piMax in decimal started out as: 14159265358979323846264338327950288419716939937511, This is: 50 digits.
piMin in decimal started out as: 14159265358979323846264338327950288419716939937510, This is: 50 digits.
(C,C)
(Q,Q)
(R,R)
(P,P)
(K,K)
(N,N)
(K,K)
(X,X)
(Q,Q)
(S,S)
(Q,Q)
(N,N)
(C,C)
(M,M)
(K,K)
(G,G)
(M,M)
(P,P)
(S,S)
(F,F)
(J,J)
(T,T)
(C,C)
(P,P)
(F,F)
(S,S)
(T,T)
(H,H)
(Q,Q)
(W,W)
(M,M)
(D,D)
(P,P)
(A,A)
(B,B)
(E,M)  Diverges after 35 good digits
(Z,R)
(E,D)
(H,Z)
(D,W)
(N,R)
(B,W)
(R,Z)
(D,H)
(I,N)
(A,U)
(F,Y)
(O,S)
(L,C)
(Y,X)

__________________________________

piMax in decimal started out as: 1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303820, This is: 199 digits.
piMin in decimal started out as: 1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819, This is: 199 digits.
(min,max)
(C,C)
(Q,Q)
(R,R)
(P,P)
(K,K)
(N,N)
(K,K)
(X,X)
(Q,Q)
(S,S)
(Q,Q)
(N,N)
(C,C)
(M,M)
(K,K)
(G,G)
(M,M)
(P,P)
(S,S)
(F,F)
(J,J)
(T,T)
(C,C)
(P,P)
(F,F)
(S,S)
(T,T)
(H,H)
(Q,Q)
(W,W)
(M,M)
(D,D)
(P,P)
(A,A)
(B,B)
(J,J)
(A,A)
(R,R)
(Y,Y)
(H,H)
(U,U)
(P,P)
(P,P)
(U,U)
(F,F)
(C,C)
(L,L)
(D,D)
(K,K)
(L,L)
(T,T)
(D,D)
(W,W)
(Q,Q)
(N,N)
(H,H)
(P,P)
(H,H)
(X,X)
(Z,Z)
(K,K)
(U,U)
(T,T)
(Y,Y)
(U,U)
(D,D)
(A,A)
(L,L)
(H,H)
(I,I)
(O,O)
(P,P)
(P,P)
(W,W)
(K,K)
(J,J)
(O,O)
(K,K)
(Q,Q)
(M,M)
(B,B)
(E,E)
(V,V)
(I,I)
(O,O)
(A,A)
(X,X)
(L,L)
(F,F)
(F,F)
(N,N)
(G,G)
(I,I)
(L,L)
(L,L)
(P,P)
(H,H)
(R,R)
(L,L)
(R,R)
(R,R)
(B,B)
(H,H)
(D,D)
(J,J)
(G,G)
(U,U)
(C,C)
(T,T)
(S,S)
(B,B)
(W,W)
(S,S)
(I,I)
(O,O)
(R,R)
(A,A)
(V,V)
(G,G)
(T,T)
(E,E)
(N,N)
(L,L)
(P,P)
(I,I)
(Z,Z)
(N,N)
(R,R)
(X,X)
(F,F)
(O,O)
(N,N)
(V,V)
(T,T)
(O,O)
(X,X)
(L,L)
(K,K)
(H,H)
(E,E)  This is the 140th decimal place.
(P,S)  min and max diverge here; digits are good above this point.
(B,I)
(X,H)
(X,Q)
(F,Y)
(X,L)
(J,S)
(Z,J)
(J,E)
(M,Z)
(E,D)
(P,J)
(W,Z)
(U,W)
(T,W)
(G,A)
(L,T)
(P,M)
(L,I)
(L,S)
(D,Y)
(Y,V)
(S,M)
(P,J)
(R,A)
(R,H)
(Q,U)
(D,Q)
(D,Y)
(Q,P)
(O,G)
(G,R)
(G,Q)
(G,Q)
(C,D)
(S,Z)
(P,S)
(E,N)
(U,X)
(H,W)
(N,Z)
(V,A)
(C,F)
(X,A)
(N,I)
(R,M)
(Q,V)
(Y,X)
(A,A)
(T,T)
(X,F)
(G,P)
(K,O)
(Y,C)
(E,V)
(Q,U)
(U,E)
(N,F)
(T,C)

__________________________________

#3559 Introductions » Winter Lover » 2005-08-29 13:32:09

John E. Franklin
Replies: 82

Hi,
I love the winter and cold weather, and I'm also pretty fond of math.  Some things in math come easy to me and some things I find very difficult and I never understood such as LaPlace Transforms and differential equations and a lot of calculus and statistics were all very hard for me.  Sometimes I will arrive at an answer through unorthodox methods, so bear with me! smile

#3560 Maths Is Fun - Suggestions and Comments » Inserting pictures: how to do it and what about disk space? » 2005-08-29 12:58:14

John E. Franklin
Replies: 5

How does one display a bitmap in a thread if it is needed to clarify the math at hand?

Should we limit the usage of bitmaps to reduce disk usage?

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