TI-Basic Vault

"Some of the most elegant, compact, speedy and accurate math programs available for the TI-83 Plus." –Weregoose

Concepts

Algebra Calculus
Completing the Square Arithmetic-Geometric Mean
Fraction Converter Binomial Theorem
Quadratic Formula Double Factorial
Gamma Function
Riemann Zeta Function
Geometry Number Theory
Heron's Formula Base Converter
Fibonacci Numbers
Statistics Unsorted
Mode Calculator

Arithmetic-Geometric Mean

Description

Computes the arithmetic-geometric mean of two numbers.

See A068521 on Sloane's OEIS.

See Arithmetic-Geometric Mean on MathWorld.

Example

{1,2:prgmAGM ⇒ 1.456791031

Program

PROGRAM:AGM
:While stdDev(Ans
:{mean(Ans),√(prod(Ans
:End
:min(Ans

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References

http://www.unitedti.org/index.php?act=findpost&pid=97318

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Base Converter

Description

Translates integers between different bases (2–35).

See A007088 through A007095 on Sloane's OEIS.

See Base on MathWorld.

Example

{16,10:prgmBASECONV
?7C
 ⇒ 124

{31,28:prgmBASECONV
?4FJL2QS3l
 ⇒ A4K56P031

Program

PROGRAM:BASECONV
:Input Str1
:Ans→A
:Ans(2→A
:"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ→Str2
:length(Str1
:sum(seq(LA(1)^(Ans-A)(inString(Str2,sub(Str1,A,1))-1),A,1,Ans→B
:"░ // one space
:For(C,1,E5×√2+log(B)/log(A
:sub(Str2,int(E5×√2+AfPart(B/A^C)),1)+Ans
:End
:Ans

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References

http://www.unitedti.org/index.php?showtopic=6803

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Binomial Theorem

Description

Lists the coefficients of (Ax+By)^N in expanded form.

See Binomial Theorem on MathWorld.

Example

1→A:2→B:3→N:prgmBINOMIAL ⇒ {1 6 12 8}

‾1→A:5→B:4→N:prgmBINOMIAL ⇒ {1 ‾20 150 ‾500 625}

Program

PROGRAM:BINOMIAL
:seq(N nCr KB^KA^(N-K),K,0,N

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References

http://www.unitedti.org/index.php?showtopic=6745

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Completing the Square

Description

Transforms the polynomial Ax²+Bx+C into A(x+B′)²+C′.

See Completing the Square on MathWorld.

Example

2→A:4→B:5→C:prgmCTSQUARE ⇒ {2 1 3}

1→A:‾5→B:6→C:prgmCTSQUARE ⇒ {1 ‾5/2 ‾1/4}

Program

PROGRAM:CTSQUARE
:.5B/A
:{A,Ans,C-AAns²►Frac

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References

http://mathworld.wolfram.com/CompletingtheSquare.html

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Double Factorial

Description

Computes the double factorial of an integer.

See A006882 on Sloane's OEIS.

See Double Factorial on MathWorld.

Example

8:prgmDBLFACT ⇒ 384

Program

PROGRAM:DBLFACT
:int((.5Ans)!√(2^Ans√((2/π)^(1-cos(πAnsr

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References

http://functions.wolfram.com/06.02.02.0001.01

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Fibonacci Numbers

Description

Computes the nth Fibonacci number.

See A000045 on Sloane's OEIS.

See Fibonacci Number on MathWorld.

Example

35:prgmFIBNACCI ⇒ 9227465

{10,11,12:prgmFIBNACCI ⇒ {55 89 144}

Program

PROGRAM:FIBNACCI
:int(round(√(.8)cosh(Anssinh‾¹(.5

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References

http://www.unitedti.org/index.php?act=findpost&pid=102484

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Fraction Converter

Description

Returns a list containing the numerator and denominator of the input.

See Fraction on MathWorld.

Example

6.375:prgmTOFRAC ⇒ {51 8}

‾.5975268:prgmTOFRAC ⇒ {‾1493817 2500000}

659438/32481527:prgmTOFRAC ⇒ {50726 2498579}

Program

PROGRAM:TOFRAC
:Ans→A
:{1,0→A
:abs(A→B
:0
:Repeat not(A-Ans‾¹round(AnsA,0
:{Ans,Ansint(B)+LA(1→A
:If fPart(B
:1/fPart(B→B
:max(LA
:End
:round(Ans{A,1

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References

http://www.unitedti.org/index.php?act=findpost&pid=114115

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Gamma Function

Description

Evaluates the gamma function for any real number argument.

See A111293 on Sloane's OEIS.

See Gamma Function on MathWorld.

Example

5:prgmGAMMA ⇒ 24

17/3:prgmGAMMA ⇒ 68.65322228

‾2.35:prgmGAMMA ⇒ ‾1.247141823

Program

PROGRAM:GAMMA
:Ans→A
:1+abs(Ans)+(Ans<0→B
:If 2≤abs(A
:Then
:sum(12‾¹/{Ans,‾30Ans³,105Ans^5,‾140Ans^7,99Ans^9
:Else
:2fnInt(tan‾¹(T/Ans)/(e^(2πT)-1),T,0,4
:End
:√(2π)e^(Ans-B)B^(B-.5)/(B-1
:If A<0
:π/(Anssin(πAr
:Ans

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References

Related Concepts

Heron's Formula

Description

Computes the area of a triangle given three side lengths.

See A070086 on Sloane's OEIS.

See Heron's Formula on MathWorld.

Example

{3,4,5:prgmHERON ⇒ 6

{5,7,8:prgmHERON ⇒ 17.32050808

Program

PROGRAM:HERON
:√(sum(.5Ans)prod(sum(.5Ans)-Ans

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References

http://www.unitedti.org/index.php?act=findpost&pid=97869

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Mode Calculator

Description

Returns the anterior mode of a list.

See Mode on MathWorld.

Example

{6,5,4,2,5,2:prgmMODE ⇒ 5

{2.5,π,‾11,√(2:prgmMODE ⇒ 2.5

Program

PROGRAM:MODE
:imag(max(Ansi+E9seq(sum(Ans=Ans(A)),A,1,dim(Ans

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References

http://www.unitedti.org/index.php?act=findpost&pid=103903

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Quadratic Formula

Description

Calculates the roots of Ax²+Bx+C=0.

See Quadratic Formula on MathWorld.

Example

1→A:3→B:2→C:prgmQUADFORM ⇒ {‾1 ‾2}

36→A:‾18→B:9/2→C:prgmQUADFORM ⇒ {.25+.25i .25-.25i}

Program

PROGRAM:QUADFORM
:‾2C/(B+{1,‾1}√(B²+4ACi²

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References

http://www.unitedti.org/index.php?act=findpost&pid=116156

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Riemann Zeta Function

Description

Evaluates the Riemann zeta function for any real number argument.

See A068469 on Sloane's OEIS.

See Riemann Zeta Function on MathWorld.

Example

3:prgmZETA ⇒ 1.202056903

‾.56:prgmZETA ⇒ ‾.1872669279

Program

PROGRAM:ZETA
:.5+(Ans-1)‾¹+2fnInt(.5/√(T²+1)^Ans(tanh(Tπ)‾¹-1)sin(Anstan‾¹(T)),T,0,4

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References

http://functions.wolfram.com/10.01.07.0009.01

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