Eddie's Math and Calculator Blog: July 2024

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Saturday, July 27, 2024

Spotlight: Texas Instruments TI-30 ECO RS: The Solar TI-30Xa

Spotlight: Texas Instruments TI-30 ECO RS: The Solar TI-30Xa

Quick Facts

Model: TI-30 ECO RS

Company: Texas Instruments

Timeline: 2015 – present (Europe

Type: Scientific calculator

Power: Solar

Display: One line, 10 digits, 2 digit exponents

Introduction

The TI-30 ECO RS is a European all-solar powered version of the battery-powered, specifically the LR44 battery, powered TI-30Xa.

Why did I get the TI-30 ECO RS? Truth be told, I am partial to solar-powered scientific calculators. I still dream of the day a solar powered (even if it is hybrid with battery) graphing calculator, that’s yet to happen. Blue is my favorite color.

Per Texas Instruments, the TI-30 ECO RS was awarded the Blue Angel award, which is a certification for the product being environmental friendly. Along with the calculator being completely solar powered, the TI-30 ECO RS is made from recycled plastic.

Features

The TI-30 ECO RS is a standard and simple scientific calculator that follows the classic TI-30 line:

* One line display, up to 10 digits. Display modes include floating pint, fixed decimal, scientific notation, and engineering notation.

* Arithmetic, powers, roots, exponential and logarithm functions

* Trigonometric functions and inverses

* Hyperbolic functions and inverses

* Fraction calculations, including fraction/decimal conversions. The maximum denominator is 999.

* One-variable statistics including mean, standard deviation, sums

* Combinations, permutations, and factorial of positive integers (up to 69)

* Polar/Rectangular and Decimal/Decimal-Minute-Second conversions

* Three memory registers (M1, M2, M3)

The TI-30 ECO RS follows the algebraic operating system and the standard order of operations is followed with a maximum of four pending operations. There is no implied multiplication.

The calculator uses postfix notation, where some one-number operations are entered after the number. For example, to calculate the sine of 30 degrees, press 30 [ SIN ] (in degrees mode). For the anti-log of 2.6, press 2.6 [ 2^nd ] [ LOG ] <10^x>.

TI-30 ECO RS vs. TI-30Xa

Even though the feature set of the TI-30 ECO RS and the TI-30Xa are the same, there are some minor differences.

* The TI-30 ECO RS is solar powered and will never require a separate battery. This is not the first time Texas Instruments implemented the solar only design, as previous models include the TI-108, TI-31, TI-30 SLR+, the classic one-line TI-36X Solar, the classic TI-36 Solar, and the BA-Solar from 1987 are some examples. In the 1980s and 1990s, Texas Instruments used technology named Anylite Technology (TM).

* Pressing the [ON/AC] button clears everything including the memory and statistics registers and resets the calculator to Degrees mode. This is consistent with classic one-line TI solar powered calculators. If you intend to store constants long-term, you may want to consider the battery-powered TI-30Xa instead.

* Calculations on the solar powered TI-30 ECO RS are slightly slower than the TI-30Xa. I am guessing that it is due to the power source.

* Since 2015, both the TI-30 ECO RS and the TI-30Xa are free the logarithm bug (Datamath).

* The TI-30 ECO RS is sold in Europe. Outside of Europe, we have to buy a TI-30 ECO RS online. I was fortunately enough to buy one from an e-bay seller in Virginia.

Source

Woerner, Joerg. “Texas Instruments TI-30 ECO RS (2015)” Datamath Calculator Museum.

Updated May 17, 2016. Accessed June 6, 2024. http://www.datamath.org/Sci/Modern/TI-30ecRS_2015.htm

“Scientific calculator TI-30 ECO RS” Texas Instruments Calculators. 1995-2024. Accessed June 7, 2024. The page is in German. https://education.ti.com/de/produkte/taschenrechner/wissenschaftliche-rechner/ti-30-eco-rs

Eddie

Friday, July 26, 2024

Update: Swiss Micros DM41X Version 2.2

Update: Swiss Micros DM41X Version 2.2

Special thanks to Bob Prosperi of the Museum of HP Calculators.

More details and download here:

https://www.hpmuseum.org/forum/thread-22066-post-189595.html#pid189595

Highlights include:

* Bug fixes with display

* Special characters are now displayed correctly in the program editor

* The volume of the screenshot sound is increased

We are in calculator update season!

Eddie

Tuesday, July 23, 2024

HP Prime Firmware Update: 15048 (Beta)

HP Prime Firmware Update: 15048 (Beta)

Information (scroll down to Post # 52 from Klaas Kuperus)- Museum of HP Calculators:

https://www.hpmuseum.org/forum/thread-22020-page-3.html

Updates:

* Key fixes in the HP Prime Python App

* Support for non-ASCII characters in Python

* Expressions, results, and user-created functions can be loaded from saved work files (I'll have to check out how work files work)

* Statistics Apps (1-Var/2-Vars): Delete rows work with entire rows

* Some crash fixes in the PPL (programming) environment

* This is Beta software, which is still under testing and development.

Download the beta firmware here:

https://www.moravia-parts.com/hp-prime/beta-b.html

Eddie

Saturday, July 20, 2024

Swiss Micros DM41X and Casio fx-CG 50: Minor Head Loss

Swiss Micros DM41X and Casio fx-CG 50: Minor Head Loss

Introduction

When a fluid, such as water, is flowing in a pipe system, energy is lost from the flow due to friction. This loss is known as head loss. The equation presented here is an equation to determine head loss occurring in pipe bends and joints (entrances and exits), which is categorized as minor loss. Minor losses are typically summarized with major losses to determine total head loss.

A formula for minor head loss is stated as:

h = C * v^2 / (2 * g)

where:

h = head loss (m)

C = coefficient

v = velocity of the fluid (m/s)

g = Earth’s gravity = 9.80665 m/s^2 (2 * g = 19.6133 m/s^2)

C = head loss coefficient (see table below)

Type # for C	Value
1. Sharp Exit	1
2. Protruding Entrance	0.8
3. Sharp Entrance	0.5
4. Round Entrance	0.1

If we fit the above table like so:

Type # for C	Value
1	1
2	0.8
3	0.5
4	0.1

Fortunately, the data above (and only the data above) can fit into the quadratic equation:

y = -0.05 * x^2 – 0.05 * x + 1.1 = -0.05 * (x^2 + x) + 1.1

where x is the type number and y is the corresponding coefficient. The assignment of type numbers is arbitrarily.

In the code for the DM41X, I use the polynomial to grab the required coefficient of the user’s choice, mapping choice 1 to C =1 for sharp exit, mapping choice 2 to C = 0.8 for protruding entrance, and so on. I got really lucky because the quadratic equation presented a perfect fit (r^2 = 1). In programming it can serve as alternative way to retrieve coefficient values (but the fit has to be perfect or near perfect with minor adjustments).

Swiss Micros DM41X Code: HEADLOS

(HP 41C compatible, no modules needed)

01 LBL^T HEADLOS

02 LBL 00

03 ^T SHARP EXIT

04 AVIEW

05 PSE

06 PSE

07 ^T PROTRUDING

08 AVIEW

09 PSE

10 PSE

11 ^T 3 SHARP ENT.

12 AVIEW

13 PSE

14 PSE

15 ^T 4 ROUND ENT.

16 AVIEW

17 PSE

18 PSE

19 ^T TYPE?

20 PROMPT

21 INT

22 STO 00 (comparison: reject if the entry is negative or greater than 5)

23 X<=0?

24 GTO 00

25 5

26 X<=Y?

27 GTO 00

28 RCL 00

29 X↑2

30 RCL 00

31 +

32 -20

33 /

34 1.1

35 +

36 ^T VEL. <M/S>?

37 PROMPT

38 X↑2

39 *

40 19.6133

41 /

42 ^T HEAD LOSS=

43 ARCL X

44 RTN

45 END

Casio fx-CG 50 Program HEADLOSS

Menu “TYPE”, “SHARP EXIT”, 1, “PROTRUDING”, 2, “SHARP ENTRANCE”, 3, “ROUND ENTRANCE”, 4

Lbl 1: 1 → C: Goto 5

Lbl 2: 0.8 → C: Goto 5

Lbl 3: 0.5 → C: Goto 5

Lbl 4: 0.1 → C: Goto 5

Lbl 5

“VELOCITY (M _| S)”? → V ( _| is the fraction character [ []/[] ] )

C × V² ÷ 19.6133 → H

“HEAD LOSS:”

Example

For the velocity, v = 10.5 ft/s ≈ 3.2004 m/s:

Type	Head Loss (h)
1. Sharp Exit	0.5222
2. Protruding Entrance	0.4178
3. Sharp Entrance	0.2611
4. Round Entrance	0.0522

Sources

Ajmera, Benna. “Engineering Formulas” Quick Study Academic. BarCharts, Inc. 2014

“Minor Losses in Pipes and Ducts“ Ansys. 2020. https://courses.ansys.com/wp-content/uploads/2020/09/Lesson-4-Minor-Losses-in-Pipes-and-Ducts-Handout.pdf Retrieved June 6, 2024.

Until next time,

Eddie

Monday, July 15, 2024

Firmware Updates: Numworks and HP Prime

Firmware Updates: Numworks and HP Prime

Good morning. Just a quick update:

Numworks: Version 23.

Highlights: Derivatives, Search Interval for Solving Equations

More information: https://www.numworks.com/calculator/update/version-23/

HP Prime: Firmware 15008 (Beta)

Highlights: Memory leak fixes, STRING fixes, Greek letters are now case-sensitive, Copying a value with nested exponents doesn't rearrange parenthesis

More information: https://www.hpmuseum.org/forum/thread-22020.html

Take care,

Eddie

Saturday, July 13, 2024

TI-84 Plus CE and Casio fx-CG 50: Mean Squared Error

TI-84 Plus CE and Casio fx-CG 50: Mean Squared Error

Introduction

The mean square error computes the mean distance from observed (y) versus predicted (y’) values. With the n data points, the standard formula for mean squared error (MSE) is calculated as:

MSE = 1 / n * Σ((y_i – y’_i)^2 for i=1 to n)

Where:

n = number of data points

y = observed points

y’ = predicted points. Any regression can be used, but the linear regression is typically used (y = a + b * x).

When MSE is small, (as closed to zero as possible), the better the data fits the regression curve. MSE is sensitive to how much data points stray from the regression line. [see Source]

TI-84 Plus CE Program: MSE

How to retrieve the statistical variables and the apostrophe character:

a: [ vars ], 5, [ → ], [ → ], 2

b: [ vars ], 5, [ → ], [ → ], 3

n: [ vars ], ,5 ,1

‘: [ 2^nd ] [ apps ] <angle>, 2

Lists used:

L1 = x data

L2 = y data

L3 = y’ (predicted y) data

Download the program here: https://drive.google.com/file/d/1toVMgznJOGdaK4uhvfrcvvb3t__D9yJD/view?usp=drive_link

Casio fx-CG 50

The Casio fx-CG 50 (and other modern Casio graphing calculators such as the fx-9750GIII/9860GIII) has a MSe variable (Mean Square Error) included in the statistics variables. However, Casio’s calculation of Mse vary depending on the regression model selected. For the linear regression mode, Mse is calculated with the following formula:

Mse = 1 / (n – 2) * Σ((y_i – y’_i)^2 for i=1 to n)

Apparently the are different approaches.

Examples (with the Presented Formula)

Linear Regression is assumed (y = a + b * x, a = y-intercept, b = slope). Results are shown using the MSE program (TI-84 Plus CE).

Set 1:

L1 = x	L2 = y
1	1.035
2	1.076
3	1.112
4	1.400
5	1.558
6	1.827

a: 0.7652666667

b: 0.1626857143

MSE: 0.0066101841

Set 2:

L1 = x	L2 = y
40	385
41	349
40	376
41	358
39	333
38	326
39	371
40	350

a: 22.1

b: 8.4

MSE: 306.85

Source

Encord. “Mean Square Error”. Encord Computer Vision Glossary. 2023. Retrieved May 25, 2024. https://encord.com/glossary/mean-square-error-mse/

Next post: Saturday, July 20, 2024

Eddie

Sunday, July 7, 2024

Numworks: Drawing Simple Shapes with Pyplot

Numworks: Drawing Simple Shapes with Pyplot

Welcome to a special edition of our blog.

The goal of today’s blog is provide templates to draw simple shapes such as ellipses, circles, rectangles, squares, equilateral triangles, and 45-45-90 right triangles. Adjust the position, screen size, and colors as you see fit.

The module is used is pyplot.

Ellipses and Circles with drawellipse.py

Draw an ellipse given the length of x and y radii. If x and y are equal, a circle is drawn. The screen is set up to fit the proportion of the 320 x 220 screen. The vertical axis ranges from y = -44 to y = 44 while the horizontal axis ranges from x = -64 to x = 64. The ellipse is centered at (0,0).

Numworks script: https://my.numworks.com/python/ews31415/drawellipse

Script: drawellipse.py

from math import *
from matplotlib.pyplot import *

print("Draw an ellipse\nusing pyplot")
a=eval(input("x axis? "))
b=eval(input("y axis? "))

# set axis
axis((-64,64,-44,44))

# set points
tl=[i/128*2*pi for i in range(129)]
xl=[a*cos(i) for i in tl]
yl=[b*sin(i) for i in tl]

# draw the ellipse
c='purple'
plot(xl,yl,c)
show()

Rectangles and Squares with drawrect.py

Draw a rectangle given its horizontal length (h) and vertical length (v). If the horizontal and vertical lengths are equal, a square is drawn. The rectangle is centered at (0, 0). The screen is set up to fit the proportion of the 320 x 220 screen. The vertical axis ranges from y = -44 to y = 44 while the horizontal axis ranges from x = -64 to x = 64.

Numworks script: https://my.numworks.com/python/ews31415/drawrect

Script: drawrect.py

from math import *
from matplotlib.pyplot import *

print("Draw a rectangle\nusing pyplot")
h=eval(input("horiz. length? "))
v=eval(input("vert. length? "))

# set axis
axis((-64,64,-44,44))

# set points
xl=[-h/2,h/2,h/2,-h/2,-h/2]
yl=[v/2,v/2,-v/2,-v/2,v/2]

# color
c='green'

# draw rectangle
plot(xl,yl,c)
show()

Equilateral Triangles with drawtrieq.py

Draws an equilateral (60-60-60) triangle. Enter the length of the side (s). The base is set on the x-axis. The screen is set up to fit the proportion of the 320 x 220 screen. The vertical axis ranges from y = -44 to y = 44 while the horizontal axis ranges from x = -64 to x = 64.

Numworks script: https://my.numworks.com/python/ews31415/drawtrieq

Script: drawtrieq.py

from math import *
from matplotlib.pyplot import *

print("Draw an equilateral triangle\nusing pyplot")
s=eval(input("side length? "))

# set axis
axis((-64,64,-44,44))

# set points
t=s*sqrt(3)/2
xl=[-s/2,s/2,0,-s/2]
yl=[0,0,t,0]

# draw the triangle
c='brown'
plot(xl,yl,c)
show()

45-45-90 Degree Right Triangles with drawtrit.py

Draws an 45-45-90 degree right triangle. Enter the length of the one of the legs (s), not the hypotenuse. The base is set on the x-axis. The screen is set up to fit the proportion of the 320 x 220 screen. The vertical axis ranges from y = -44 to y = 44 while the horizontal axis ranges from x = -64 to x = 64.

Numworks Script: https://my.numworks.com/python/ews31415/drawtrirt

Script: drawtrit.py

from math import *
from matplotlib.pyplot import *

print("Draw a 45-45-90 triangle\nusing pyplot")
s=eval(input("short length? "))

# set axis
axis((-64,64,-44,44))

# set points
xl=[-s/2,s/2,-s/2,-s/2]
yl=[0,0,s,0]

# draw the triangle
c='blue'
plot(xl,yl,c)
show()

Enjoy and I hope you find these scripts useful in your drawing scripts.

Eddie

Saturday, July 6, 2024

HP 12C: Hyperbolic Sine and Cosine, and their Inverses

HP 12C: Hyperbolic Sine and Cosine, and their Inverses

Introduction

The following program calculates four hyperbolic functions:

sinh x = (e^x – e^(-x)) / 2

cosh x = (e^x + e^(-x)) / 2

arcsinh x = ln(x + √(x^2 + 1))

arccosh x = ln(x + √(x^2 - 1)) (principal arccosh x)

HP 12C Program: sinh x, cosh x, arcsinh x, arccosh x

Step #: Step Code: [ keys ]

# sinh x: GTO 01, R/S

01: __, 43, 22: [ g ] e^x

02: __, 43, 36: [ g ] LST x

03: __, __, 16: [ CHS ]

04: __, 43, 22: [ g ] e^x

05: __, __, 30: [ - ]

06: __, __, _2: [ 2 ]

07: __, __, 10: [ ÷ ]

08: 43, 33, 00: [ g ] GTO 00

# cosh x: GTO 09, R/S

09: __, 43, 22: [ g ] e^x

10: __, 43, 36: [ g ] LST x

11: __, __, 16: [ CHS ]

12: __, 43, 22: [ g ] e^x

13: __, __, 40: [ + ]

14: __, __, _2: [ 2 ]

15: __, __, 10: [ ÷ ]

16: 43, 33, 00: [ g ] GTO 00

# arcsinh x: GTO 17, R/S

17: __, __, 36: [ ENTER ]

18: __, __, 36: [ ENTER ]

19: __, __, _2: [ 2 ]

20: __, __, 21: [ y^x ]

21: __, __, _1: [ 1 ]

22: __, __, 40: [ + ]

23: __, 43, 21: [ √ ]

24: __, __, 40: [ + ]

25: __, 43, 23: [ g ] LN

26: 43, 33, 00: [ g ] GTO 00

# arccosh x: GTO 27 R/S

27: __, __, 36: [ ENTER ]

28: __, __, 36: [ ENTER ]

29: __, __, _2: [ 2 ]

30: __, __, 21: [ y^x ]

31: __, __, _1: [ 1 ]

32: __, __, 30: [ - ]

33: __, 43, 21: [ √ ]

34: __, __, 40: [ + ]

35: __, 43, 23: [ g ] LN

36: 43, 33, 00: [ g ] GTO 00

Instructions

1. Enter x

2. To calculate, press [ g ] GTO ##, then press [ R/S ].

* GTO 01 R/S: sinh x

* GTO 09 R/S: cosh x

* GTO 17 R/S: arcsinh x

* GTO 27 R/S: arccosh x

Examples

(Fix 4)

x	sinh x	cosh x
-0.64	-0.6846	1.2119
0.59	0.6248	1.1792
1.23	1.5645	1.8568
3.74	21.0371	21.0609

Note: arccosh(1.2119) returns 0.64

Source

Selby, Samuel M. Ph. D. Sc. D. CRC Standard Mathematics Tables: Nineteenth Edition. The Chemical Rubber Co. Cleveland, OH. 1971. pp. 202, 211

Until next time,

Eddie