Fun With The HP 27S
Notes:
* The HP 27S is set to FIX 4
* Since none of the formulas have trigonometric functions, they can also be programmed on the HP 17B and HP 17BII+
Partial Fraction Decomposition
(A ∙ x + B)÷((x + C) ∙ (x + D)) = R÷(x + C) + S÷(x + D)
Inputs: A, B, C, D
Outputs: R, S
Formula:
PARTFRAC2:(A+B+C+D)×0=IF(S(R):(B-C×A)÷(D-C)-R:(B-D×A)÷(C-D)-S)
Example: (4 ∙ x + 3) ÷ ((x - 5) ∙ (x + 1))
A = 4, B = 3, C = -5, D = 1
Results: R = 3.8333, S = 0.1667
Use that the 0×(var1+var2+...) to set an order of variables in the solver.
2 x 2 Simultaneous Equations
A ∙ x + B ∙ y = C
D ∙ x + E ∙ y = F
The solutions are:
x = (C ∙ E - B ∙ F) ÷ (A ∙ E - B ∙ D)
y = (A ∙ F - C ∙ D) ÷ (A ∙ E - B ∙ D)
Formula:
SIM2X2:0×(A+B+C+D+E+F+L(M:A×E-B×D))=IF(S(X):(C×E-B×F)÷G(M)-X:(A×F-C×D)÷G(M)Y)
Example: 2x + 3y =5, -3x + 8y = -8
A = 2, B = 3, C = 5, D = -3, E = 5, F = -8
Results: X = 2.5789, Y = -0.0526
Floor Function
floor(x): the greatest integer less than or equal to x
floor(x):
If frac(x) = 0 Then return x
Else If x≥0, then return intg(x) else return intg(x)-1
Formula:
FLOOR=IF(FP(X)=0:X:IF(X>=0:IP(X):IP(X)-1))
Examples:
X = 2.38, FLOOR = 2.0000
X = -9.21, FLOOR = -10.0000
Ceiling Function
ceil(x): the least integer greater than or equal to x
ceil(x):
If frac(x) = 0 Then return x
Else If x≥0, then intg(x)+1 else return intg(x)
Formula:
CEIL=IF(FP(X)=0:X:IF(X>=0:IP(X)+1:IP(X)))
Examples:
X = 2.38, CEIL = 3.0000
X = -9.21, CEIL = -9.0000
Rydberg Formula
The Rydberg formula measures the light's wavelength when an electron moves between energy quantum numbers (from higher to lower levels). The Rydberg formula is to be used for simple atoms only, and is most used for hydrogen atoms.
1/λ = R ∙ Z^2 ∙ (1/n1^2 - 1/n2^2)
R = Rydberg's Constant ≈ 1.097373157 × 10^7 m^(-1)
Z = atomic number, 1 for hydrogen
n1, n2: energy levels
Formula:
RYDBERG:INV(L)=1.09737316E7×SQ(Z)×(INV(SQ(N1))-INV(SQ(N2)))
N2 > N1
Example:
The energy of an hydrogen election from level 4 to level 2. Z = 1
Z =1, N1 = 2, N2 = 4
Result: L = 4.8601E-7
Source:
Helmenstine, Todd. "What Is the Rydberg Formula and How Does It Work?" ThoughtCo, Aug. 28, 2020, https://www.thoughtco.com/what-is-the-rydberg-formula-604285 Retrieved November 4, 2021
Moment of Inertia - Circular Ring
D$OUT: outside diameter
D$IN: insider diameter. For a circle, set D$IN = 0
I: moment of inertia
Formula:
I=PI×(D$OUT^4-D$IN^4)÷64
Examples:
Circular Ring:
D$OUT = 6.2, D$IN = 1.9; I = 71.8935
Circle:
D$OUT = 6.2, D$IN = 0; i = 72.5332
Source:
"Properties Of Annual Sections" HP-19C/HP-29C Solutions: Civil Engineering Hewlett-Packard. 1977
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