Eddie's Math and Calculator Blog: June 2021

Monday, June 28, 2021

Calculos: Mathematics Calculation Game (Kickstarter)

Calculos: Mathematics Calculation Game (Kickstarter)

The Card Game

Xavier Wilain created the card game Calculos, which is based on quick, mental mathematics dealing with the four arithmetic operations: addition, subtraction, multiplication, and division. There is a mixed version that has all four arithmetic operations.

Players start with a card and try to find a calculation that matches any of the calculations on the center card.

For example, if the center card has:

2 × 5

3 × 6

5 × 5

4 × 4

If you have any of the calculations on your card, say 4 × 4, you shout "4 times 4 equals 16" and claim the card. The object is for find a calculation faster than their opponents.

Here is a video of the card game and how to play it:

https://www.youtube.com/watch?v=-PEfEVTV4wI

The card game comes in four levels: each level has a different set of calculations on the card, from four to eight. On the XW_SeriousGames website, each level can be purchased separately or altogether for each operation.

Link: https://www.xwseriousgames.com/

The Mobile App (Kickstarter)

Wilain is running a Kickstarter campaign to adapt the card game into a mobile app that contains all 20 levels (4 four levels for each arithmetic operation plus one for mixed) with plans to add levels in the future. Wilain has goal to raise 33'000 CHF (Swiss Francs, which is $35,897.63 in US Dollars on 6/28/2021 - conversion provided by Morningstar). If successful, the mobile app is set to begin development in October 2021. The target fund date is July 27, 2021.

Kickstarter page:

https://www.kickstarter.com/projects/xw-serious-games/calculos/description

Please check this game out, it promises to be a great way to strength our mental calculation skills.

Eddie

All original content copyright, © 2011-2021. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Review: Calculated Industries ElectricCalc Pro (Model 5070)

Review: Calculated Industries ElectricCalc Pro (Model 5070)

Quick Facts

Model Number: 5070

Company: Calculated Industries

Year of Production: 2014 - present

Operating System: Chain

Batteries: 1 x CR 2016

Memory Register: 1 independent (M), memories M1 - M9

Upgradable Chip: Base Model is set for 2014, chips are available for 2017 and 2020 (and I presume 2023 given how often NEC updates their code)

Cost: Retail: $99.95, but sells for anywhere from $59 to as high as $129. Do your shopping carefully!

Product Page: https://www.calculated.com/mobile/prd160/ElectriCalc-Pro-5070-Electrical-Code-Calculator.html

Make Sure Your ElectricCalc Is Up to Code

Bought new or in box, the calculator comes in a blue Armadillo Gear case. Often, the ElectricCalc Pro comes with the latest chip (2020) already installed or in my case, my calculator had the 2017 chip installed and the 2020 chip in a separate package. Installation is simple and you just need a Phillips screwdriver.

Currently, the ElectricCalc handles code for the following years:

1996

1999

2002

2005

2008

2011

2014

2017 (2017 or 2020 chip required)

2020 (2020 chip required)

Set your jurisdiction by pressing [ Set ] [ ÷ ]. The first preference is the NEC, which you can scroll by pressing [ + ] and [ - ].

Many calculations depend on the NEC code such as wire size, voltage drop, ground conductor wire size, and conduit sizes for wires. Many of the calculations display the reference table. Because of the stored values for the NEC codes, the ElectricPro already proves its value.

Wire Insulation can be selected:

[ Set ] [ 7 ]: 75°C wire insulation (167°F)

[ Set ] [ 9 ]: 90°C wire insulation (194°F)

[ Set ] [ 6 ]: 60°C wire insulation (140°F)

We can work with copper and aluminum wires with the [ Set ] [ 4 ] toggle.

Ohm's and Kirchhoff's Law

The ElectricCalc Pro has the following keys to work with Ohm's Law:

[ Set ] [ V ] ( R ): Resistance in Ohms (Ω)

[ Set ] [ Volts ] (Vdc): Voltage in Volts (V)

[ Set ] [ Amps ] (Idc): Current in Amps (A)

Likewise, the keys work with Kirchhoff's Law:

[ VA ]: Volt-Amps

[ Volts ]: Voltage in Volts (V)

[ Amps ]: Current in Amps (A)

1 Phase vs 3 Phase

Select 1 Phase mode by pressing [ Set ] [ 1 ]. For 3 Phase, press [ Set ] [ 3 ].

What is great about the ElectricCalc Pro, the settings will be displayed at all times.

Verdict

The keyboard of the ElectricCalc Pro work well and the keys give good feedback. Like the other Calculated Industries calculators, the calculators hold data specific to the industry.

And like the Calculated Industries calculators, having the ElectricCalc Pro opens up a new world of knowledge. I'm glad to have the calculators in my collection.

Eddie

Sunday, June 27, 2021

Review: Victor 6500 Loan Calculator, HP 48G Retro Month

Review: Victor 6500 Loan Calculator, HP 48G Retro Month

Victor 6500 Review

Quick Facts

Company: Victor

Year Introduced: about 2010, still in production

Battery: Solar and 1 AA battery

Digits: 12

Memory Registers: 2: Independent (M) and Grand Total (GM)

Cost: About $20.00 to $25.00 US

Product Page: https://www.victortech.com/product/6500

It is rare that a desktop calculator features advanced financial or scientific functions, and that is what attracted me to the Victor 6500. The keys respond quickly which allows for fast typing. The display has room for 12 large digits which makes reading the display easy.

Features

* Fix Display Switch: Float, 0, 2, 4, Add Mode

* Round Setting Switch: cut (always round results down), 5/4 (regular rounding rules are followed), up (always round up)

* Time Value of Money - will be discussed next

* %, Δ%, √

* Tax Rate: setting, TAX+, TAX-

* Double Zero Key

Memory Registers

There are two memory registers:

Independent Memory (M). This the traditional memory register that comes with most desktop calculators. Included are M+ and M-. Recall and clear are combined in one key RCM.

Grand Total (GT). The grand total memory is activated every time the equals key is pressed.

Time Value of Money

The Victor 6500 have four finance keys:

Loan = PV

Pmt = Payment

Years = number of years = n * PYR

Int = annual interest rate

The cash flow convention (inflow/outflow) is not followed, all results are positive. The number of payments per year is set through the P/Y setting.

What is missing is the FV (future value) key, which leaves out some of the finance problems involving calculating balance or balloon payment. However, we can still do a lot of calculations on the Victor 6500 fairly easier. Here are several example calculations. In these examples, the Victor 6500 is set to 2 Decimal Places with 5/4 rounding mode.

Example 1: Calculating Payment of a Loan

Loan: 345,000.00

Years: 30

Interest Rate: 3.3%

[ ON/C ] [ ON/C ]

345000 [ Loan ]

30 [ Years ]

3.3 [ Int ]

[ Pmt ] returns 1,510.95

Example 2: Calculating Payment of a Loan with a Down Payment

Loan: 260,000.00 with 15% down

Years: 27

Interest Rate: 3.2%

[ ON/C ] [ ON/C ]

260000 [ - ] 15 [ % ] [ Loan ]

27 [ Years ]

3.2 [ Int ]

[ Pmt ] returns 1,019.53

Example 3: PITI (Payment with Principal Interest Taxes Insurance)

Loan: 300,000.00

Years: 30

Interest Rate: 3.25%

Annual Property Tax: 2,121.00

Annual Property Insurance: 541.00

[ ON/C ] [ ON/C ] [ MRC ] [ MRC ]

300000 [ Loan ]

30 [ Years ]

3.25 [ Int ]

[ Pmt ] [ M+ ]

2121 [ + ] 541 [ = ] [ ÷ ] 12 [ = ] [ M+ ]

[ MRC ] (once)

PITI: 1527.45

Verdict

I like the Victor 6500 since it offers a time value of money solver on a desktop calculator form. I wish Victor would have included the future value variable. The keys are fast and responsive. The keyboard is pretty light but also feel stable.

I am working on posting additional examples for the Victor 6500 in the near future.

HP 48G Retro Month - July 2021

For the month of July 2021, every Saturday from July 10 to July 31 will have a post on the legendary HP 48G/48GX/48G+ calculator.

Next post will be on July 10, 2021 (taking the Fourth of July weekend off). Have a great day and thank you!

Eddie

Saturday, June 26, 2021

7000G Retro Month - June 26 Edition

7000G Retro Month - June 26 Edition

Introduction

Welcome to the 7000G Retro Month, which features programming for the classic Casio calculators from the mid/late 1980s: primarily fx-7000G and fx-7500G. Since the programming language stays similar throughout the years, programs can be translated to the fx-6300G and later graphing calculators with little to no adjustments. Non graphic programs should be ported to the fx-4000P, fx-4500P (A), fx-3650p (II), fx-50F Plus (II), and fx-5800P with little to no adjustments.

7000G Retro Month takes place every Saturday during June 2021.

To make text easier to type, I can going to use the following text friendly symbols for the following:

-> for →

/I for ⊿

=> for ⇒

What do you think? Unicode or simple text equivalents?

- - - - - - -- - -- - -

Today's subject revolves around Calculus. Enjoy!

- - - -- - - -- - -- -- -

The three programs listed here call another program as a subroutine. I use Prog 0 as a subroutine.

Prog 0

[insert f(x) here]

Example: Prog 0 contains X^2+4. The results gets stored in in Ans.

Sum

S = ∑( f(x), X = A to B)

"A"? -> A

"B"? -> B

A -> X

0 -> S

Lbl 1

Prog 0

Ans + S -> S

X + 1 -> X

X≤B => Goto 1

Numeric Derivative - Simple Approximation

f'(x) ≈ (f(x+h) - f(x-h))/(2h), h = tolerance (default to 10^-5)

The derivative is stored in the variable D.

"X0"? -> Z

Z+10^-5 -> X : Prog 0 : Ans -> A

Z-10^-5 -> X : Prog 0 : Ans -> B

(A-B)÷(2 10^-5) -> D

Definite Integral - Simpson's Rule

∫ f(x) dx ≈ h/3 * (y_a + ∑(4*y_odd + 2*y_even) + y_b)

where h=(b-a)/n (n is even)

The integral is stored in the variable I.

"A"? -> A

"B"? -> B

"N"? -> N

A -> X

Prog 0

Ans -> I

(B-A)÷N -> D

N÷2 -> K

Lbl 2

X+D -> X : Prog 0 : I + 4 Ans -> I

X+D -> X : Prog 0 : I + 2 Ans -> I

K - 1-> K

K≠0 => Goto 2

B -> X : Prog 0 : (I - Ans)D÷3 -> I

Eddie

Tuesday, June 22, 2021

Update: HP Prime Connectivity Kit and Emulator

Update: HP Prime Connectivity Kit and Emulator

The HP Prime Connectivity Kit and Emulator have been updated. The version number is 14592 (6/9/2021). Download them from this page:

https://www.hpcalc.org/prime/pc/

The 14588 (5/5/2021) firmware is still the current firmware for the HP Prime, which can be downloaded from the same page.

As a reminder, the newest firmware introduces, among other things, the Python app to the HP Prime. Click on this link to read about some of the new features: http://edspi31415.blogspot.com/2021/05/hp-prime-firmware-update-beta-python.html

Eddie

Monday, June 21, 2021

Retro Review: Sharp EL-8131

Retro Review: Sharp EL-8131

Many thanks to Christopher Brame for sending and giving me this calculator. Thank you, my friend.

Quick Facts:

Company: Sharp

Year Introduced: 1977, in production to 1978

Type: Four Function

Batteries: 2 x AA batteries

Display: 8 digits

Background

The Sharp EL-8131 is a four function function from the 1970s with classic green digits in the display. The calculator is nice and compact and held in one hand, while the other hand operates the well-designed keys.

The functions of the EL-8131 include:

* Arithmetic

* Memory: Store ( x→M), clear, recall, M-, M+

* Square Root

* Percent

What is missing is the change sign key. This presents a challenge when calculating with negative numbers.

With any four function calculators, calculations are executed in the order you press the keys.

Source:

"Sharp EL-8131 Handheld Electronic Calculator" National American of American History. Behring Center. Washington, D.C. https://americanhistory.si.edu/collections/search/object/nmah_334546 Retrieved May 23, 2021

Eddie

Sunday, June 20, 2021

TI-84 Plus CE: Bode Plots of Transfer Functions

TI-84 Plus CE: Bode Plots of Transfer Functions

Introduction

The problem BODEPLOT (2021) plots the Bode plot of a transfer function in the form:

f(s) = ( (s - z1) (s - z2) (s - z3) * ... ) / ( (s - p1) (s - p2) (s - p3) * ... )

where:

z_i = zeros of the transfer function

p_i = pole of the transfer function

s = jw

j = i = √-1

w = frequency

The plot uses a linlog plotting where each x is replaced with 10^x. The y axis represents the conversion y = 20 log_10 ( abs f( 10^x * j) ).

Lists used:

L1: list of zeros

L2: list of poles

L3: x

L4: 20 log_10 ( abs f( 10^x * j) )

You can review the zeros and poles after each entry. Erasing zeros and poles will erase the latest entry.

TI-84 Plus CE Program: BODEPLOT

Version 5.3 and above

"EWS 2021-05-02"

ClrHome

Disp "TRANSFER FUNCTION","F(S)=(S-ZERO).../(S-POLE)","S=JW 10^(W),20log(abs())"

Pause

a+bi

0→A

0→B

0→Z

Lbl 0

toString(A)+" ZEROS, "+toString(B)+" POLES"

Menu(Ans,"ADD ZERO",1,"ADD POLE",2,"ERASE LAST ZERO",3,"ERASE LAST POLE",4,"REVIEW",5,"PLOT",6)

Lbl 1

Input "ZERO? ",S

If A=0

{S}→L1

If A>0

augment(L1,{S})→L1

A+1→A

Goto 0

Lbl 2

Input "POLE? ",S

If B=0

{S}→L2

If B>0

augment(L2,{S})→L2

B+1→B

Goto 0

Lbl 3

If A>1

Then

A-1→A

A→dim(L1)

Else

0→A

DelVar L1

End

Goto 0

Lbl 4

If B>0

Then

B-1→B

B→dim(L2)

Else

0→B

DelVar L2

End

Goto 0

Lbl 5

ClrHome

If A>0

Then

Disp "ZEROS:"

Pause L1

End

If B>0

Then

Disp "POLES:"

Pause L2

End

Goto 0

Lbl 6

For(I,-6,6)

1→N

If A>0

prod(i*10^(I)-L1)→N

1→D

If B>0

prod(i*10^(I)-L2)→D

If Z=0

Then

{I}→L3

{20log(abs(N/D))}→L4

1→Z

Else

augment(L3,{I})→L3

augment(L4,{20log(abs(N/D))})→L4

End

FnOff

PlotsOff

-7→Xmin

7→Xmax

1→Xscl

min(L4)-.5→Ymin

max(L4)+.5→Ymax

10→Yscl

Plot1(xyLine,L3,L4)

PlotsOn 1

DispGraph

You can download the zip file here.

Examples

f(s) = 1/(s-3)

Poles: { 3 }

f(s) = s-0.5

Zeros: { 0.5 }

f(s) = ((s+2)(s-2))/((s-1)(s-3))

Zeros: { -2, 2 }

Poles: { 1, 3}

f(s) = (s-4)/((s+1)(s-3))

Zeros: { 4 }

Poles: { -1, 3 }

Eddie

Saturday, June 19, 2021

7000G Retro Month - June 19 Edition

7000G Retro Month - June 19 Edition

Introduction

7000G Retro Month takes place every Saturday during June 2021.

To make text easier to type, I can going to use the following text friendly symbols for the following:

-> for →

/I for ⊿

=> for ⇒

What do you think? Unicode or simple text equivalents?

- - - - - - -- - -- - -

Today's subject revolves around Probability and Random Numbers. Enjoy!

- - - -- - - -- - -- -- -

Random Integers: Repeats Allowed

This program allows the user to generate a number of integers between A and B, repeats are allowed. Each integer is displayed one at a time.

"A"? -> A

"B"? -> B

"N"? -> N

Lbl 1

Int ((B-A+1) Rnd#) /I

Dsz N

Goto 1

Combinatorics

The program allows the user to choose between three options:

1. PERM: permutation: nPr

2. COMB: combination: nCr

3. COMB REPLACE: combination with replacements allowed (n+r-1)Cr

"N"? -> N

"R"? -> R

"1. PERM"

"2. COMB"

"3. COMB REPLACE"

? -> K

K=1 => N!÷(N-R)! -> X

K=2 => N!÷(R!(N-R)!) -> X

K=3 => (N+R-1)!÷(R!(N-1)!) -> X

Binomial Distribution

This program calculates the sum of probabilities for a binomial distribution:

total probability = ∑( nCr(N,K) p^K (1-p)^(N-K), K=A to B)

Probability: 0 < p < 1

"A"? -> A : "B"? -> B

"N"? -> N : "P"? -> P

0 -> M : Lbl 1

M+(N!×P^A×(1-P)^(N-A))÷(A!(N-A)!) -> M

A+1 -> A

A>B => Goto 2

Goto 1

Lbl 2

Confidence Interval

This program generates a confidence interval using one of four probabilities are assigned to the following variables:

F: 99% (z* ≈ 2.576)

G: 98% (z* ≈ 2.326)

H: 95% (z* ≈ 1.96)

I: 90% (z* ≈ 1.645)

interval = mean ± z* × variance / √n

"CONF INTERVAL"

2.576 -> F

2.326 -> G

1.96 -> H

1.645 -> I

"MEAN"? -> A

"VAR"? -> B

"N"? -> N

"F=.99, G=.98"

"H=.95, I=.90"

? -> J

A-JB÷√N -> E /I

A+JB÷√N -> F

E: low, F: high

Eddie

Monday, June 14, 2021

Review: Calculated Industries Pipes Pro (Model 4095)

Review: Calculated Industries Pipes Pro (Model 4095)

Quick Facts

Model Number: 4095

Company: Calculated Industries

Year of Production: 2009 - present

Operating System: Algebraic (AOS) or Chain

Batteries: 2 x LR 44

Memory Register: 1 independent (M), 9 registers M1-M9

Paperless Tape Memory: 30 steps

Bought new or in box, the calculator comes in a red Armadillo Gear case that fits the calculator. I really am a fan of the Armadillo Gear cases, not only it gives the calculator protection, it makes it look better.

Product Page: https://www.calculated.com/mobile/prd267/Pipe-Trades-Pro-4095-Advanced-Pipe-Trades-Calculator.html

Mathematical Functions and Order of Operations

* Parenthesis

* Powers and Roots

* Trigonometry: Sine, Cosine, Tangent, and their inverses. All angles are in degrees.

The Pipe Trades Pro (4095) has the same operating system as the Tradesman Calc (4400), the order of operations is followed:

1. Parenthesis

2. Roots, Powers, Percent, Trigonometric Functions

3. Multiplication and Division

4. Addition and Subtraction

The Pipe Trades Pro can be set to Chain mode or Algebraic (Order) mode in preferences.

Dimensional Math

The most common feature across CI calculators (except for the finance models) is dimensional math. The dimensions the Pipe Trades Pro include are:

⦁ Feet-Inch-Fractions of Inches vs. Meters

⦁ Pounds vs Kilograms

⦁ Cubic Feet per Minute (cfm), Cubic Feet per Second (cfs), Gallons per minute (gpm), Liters per second (l/s)

⦁ Degrees Celsius vs Degrees Fahrenheit

Conversions are made by using the [ Conv ] button. Dimensional math is made quick and easy, one of the trademarks of the CI calculators.

The [ Circle ] key calculates the area and circumference of a circle given its diameter.

Right Triangle Solutions

With the right triangle keys, the Pipes Trade Pro allows the user to easily make simple offset calculations.

Angle: angle between vertex on the x-axis, in degrees

Run: length of x

Offset: length of y

Travel: hypotenuse

Comparison of CI calculators - Right Triangle Solutions Key

Pipe Trade Calculations

Now I am going to highlight some of the common calculations that are unique to this calculator. Please see the product page for a complete list of calculations because the Pipe Trades Pro does a lot more.

Pipe Size Database

The [ Pipe Mat’l ] and [ Conv ] [ Pipe Size ] (Pipe Mat’l) access the calculator’s database of pipe materials depending on material. The schedules available depend on the material selected:

1. Steel

2. Stainless Steel (S.Steel)

3. Brass

4. Aluminum (AL.)

5. Cast Iron (CAST)

6. Plastic

7. Copper

The [ Pipe Size ] key gives the outside diameter, inside diameter, wall thickness, weight per foot, filled weight per foot, and internal area in square inches. (this assumes default selections are made)

Example: 5 inch Stainless Steel pipe, class 40

Press [ Pipe Mat’l ] until S.Steel appears

Press [ Conv ] (Pipe Type) [ Pipe Size ] until 40 TYPE S.Steel appears

5 [ Inch ] [ Pipe Size ] (keep on pressing [ Pipe Size ] )

40 SIZE 5 INCH

OD 5.5673 INCH (outside diameter)

ID 5.047 INCH (inside diameter)

THK 0.258 INCH (thickness)

MATL S.STEEL

PIPE 14.90996 LB PER FEET (pipe weight per foot)

FILL 23.58304 LB PER FEET (filled weight per foot)

AREA 20.00583 SQ INCH (internal area)

(the cycle repeats)

A list of the schedules and materials available are listed on page 53 of the User Manual. The manual can be downloaded here: https://www.calculated.com/UGFiles/UG4095E-D.pdf

Elbow Calculations

The Pipe Trades Pro offers four types of elbow type problems:

1. BW-L: Butt Weld - Long

2. BW-S: Butt Weld - Short

3. FC-L: Field Cut - Long

4. FC-S: Field Cut - Short

The below type affects take out calculations.

Example: We have a butt weld-long elbow type pipe, with size of 16 inches and bend angle of 36°.

Press [ Conv ] (Elbow Type) and press [ Pipe Mat’l ] until BW-L EL. TYPE appears.

16 [ Pipe Size ]

36 [ Angle/Slope ]

Press [ Conv ] [ Angle/Slope ] (T.O./Arc) and then [ Angle/Slope ] repeatedly to get the following results:

TO 7 13/16 INCH (take-out)

IARC 10 1/16 INCH (inside arc length)

CARC 15 1/16 INCH (central arc length)

OARC 20 1 / 8 INCH (outside arc length)

For simple offset calculations, use the [ Angle/Slope ], [ Offset ], [ Run ], and [ Travel ] keys.

Pressure Loss

We can calculate the area, flow rate, and pressure loss.

n [ (dimensions) ] [ Pipe Size ] enters pipe size

n [ Conv ] [ ( ] (Flow) enters the flow rate

[ Conv ] [ √x ] (Area) gives the area

[ Conv ] [ Circle ] (Pressure) with repeated press of the [ Circle ] key pressure loss in different units

Example:

Calculate the area and pressure loss of a steel pipe of 5”, schedule 80. The flow rate is measured to be 6.2 gallons per minute.

Press [ Pipe Mat’l ] until the screen shows Steel

80 [ Conv ] [ Pipe Size ] (Pipe Type) to set the Pipe to Schedule 80

5 [ Inch ] [ Pipe Size ]

6 [ Conv ] [ 1 ] (gpm) [ Conv ] [ ( ] (Flow)

[ Conv ] [ Circle ] (Pressure) and them press [ Circle ] to cycle between units:

PSI PER FEET: 0.000008

REY 3942.518

PSF PER FEET 0.001081

inHG PER FEET 0.000015

HEAD PER FEET 0.000017

BAR PER FEET 0.000001

KPA PER FEET 0.000052

PSI PER FEET 0.000008

Verdict

The keyboard of the Pipe Trades Pro works well and the keys give good feedback.

I think the biggest benefits of the Pipe Trades Pro are the dimensional math features and types of data stored in pipe materials, pipe types, schedules, and elbow types. This, I believe, is where Calculated Industries separates itself from the rest.

I also like the extensive set of scientific calculator functions that the Pipe Trades Pro.

I plan to add more Calculated Industries calculators to my collection over the next few months, including the GradeMatic 200, ElectricCalc Pro, and the ConcreteCalc.

I plan to add more Calculated Industries calculators to my collection over the next few months.

Eddie