## Sunday, September 27, 2020

### Financial Calculators: Deferred Mortgages: Solving for Payment and Price

Financial Calculators:  Deferred Mortgages: Solving for Payment and Price

Finance Now, Pay Later!

When a customer financing a loan or mortgage, and the customer can enjoy the benefits for a period of months prior to being required to make the first payment, we are dealing with a deferred mortgage.   Interest is accrued from the beginning of the mortgage.

The procedures outlined on this blog entry can be applied to any financial calculator* with time value of money keys, such as the HP 12C and the HP 10bII+ (see source below).

* The procedure should be fine for most financial calculators.   Check your manual for details.

Deferred Mortgage:  Finding The Monthly Payment

Part 1:

Set the calculator to END mode.

N:  Enter the number of deferred payments minus 1

I:   Enter the interest rate of the loan

PV:  Enter the borrowed amount as a negative number

PMT:  Set to 0

Solve for FV

Part 2:

PV = FV from part 1   ( RCL FV, STO PV )

N:  Enter the number of payments of the term

I = interest rate of the loan

FV:  Enter the balloon payment as a negative number.  If there is no balloon payment, enter 0.

Solve for PMT, this is your payment of the deferred mortgage.

Example 1:

A homeowner finances a house for \$455,000.00.   The mortgage lasts for 30 years at 2.86%.   No payment is due for the first six months of the mortgage.

Part 1:

N: 6 -1 = 5

I:  2.86% annual rate, about 0.24% per month

PV:  -455000.00

PMT:  0.00

FV = 460447.99

Part 2:

PV:  460447.99

N:  30* 12 = 360

I:  2.86% annual rate, about 0.24% per month

FV:  0.00

PMT = -1906.67

The monthly payment is \$1,906.67.

Example 2:

A homeowner purchases a fixer-up property for \$149,000.00.  The buyer secures a 15-year mortgage at 4%.  The end of the loan requires a \$1,000.00 balloon payment but allows the buyer to defer the first payment for five months.

Part 1:

N:  5 - 1 = 4

I:  4% annual rate, about 0.33% per month

PV:  -149000.00

PMT: 0.00

FV = 150996.62

Part 2:

PV:  150996.62

N:  15 * 12 = 180

I:  4% annual rate, about 0.33% per month

FV: -1000.00

PMT = -1112.84

Deferred Payment:  Calculating the Price of the Mortgage

Part 1:

Set the calculator to END mode.

N:  Enter the number of payments of the term

I:   Enter the interest rate of the loan

PMT: Enter the payment as a positive number

FV: Enter the balloon payment as a positive number.  If there is no balloon payment, enter 0.

Solve for FV

Part 2:

FV = PV from part 1   ( RCL PV, STO FV )

N:  Enter the number of deferred payments minus 1

I = interest rate of the loan

Set PMT to 0

Solve for PV, this is your price of the deferred mortgage.

Example 3:

An owner enters a lease which requires at monthly payment of \$495.00.  The lease lasts for 8 years at 6.69%.  There is no balloon payment at the end of the lease.  The lease allowed the owner to defer the first required payments for three months.  What is the value of the lease?

Part 1:

N:  8 * 12 = 96

I:  6.69% annual rate, about 0.56% per month

PMT:  495.00

FV:  0.00

PV = -36721.17

Part 2:

FV:  -36721.17

N:  3 - 1 = 2

I:  6.69% annual rate, about 0.56% per month

Set PMT to 0

PV = 36315.13

The value of the lease is \$36,315.13.

Example 4:

An owner executes a 30-year, 3% mortgage with the required payment of \$1,005.85.  The mortgage allows for the first payment to be deferred for six months.  A \$1,000.00 balloon payment is required.  What is the price of the mortgage?

Part 1:

N:  30 * 12 = 360

I:  3% annual rate, 0.25% per month

PMT:  1005.85

FV:  1000.00

PV = -238983.97

Part 2:

FV:  -238983.97

N:  6 - 1 = 5

I:  3% annual rate, 0.25% per month

Set PMT to 0

PV = 236018.94

The value of the lease is \$236,018.94.

And that is how we work with deferred mortgages.

Source:

Greynolds Jr., Elbert B. and Aronofsky, Julius S.  Practical Real Estate Financial Analysis: Using The HP 12C Calculator:  A Step-by-Step Approach   Real Estate Education Company: Dearborn Financial Publishing, Inc.  1983.  ISBN 0-88462-378-5

Eddie

All original content copyright, © 2011-2020.  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.

## Saturday, September 26, 2020

### Retro Review: TI-36 Solar

Retro Review:  TI-36 Solar

Just the Facts:

Model:  TI-36 Solar

Company: Texas Instruments

Type: Scientific

Display:  10 digit with 2-digit exponents

Battery:  Solar

Logic: AOS

Memory Registers: 1

Years: 1984-1990

Features:

*  Complex Number Arithmetic

*  Rounding Numbers (to fixed number setting)

*  Base Conversions

*  Normal Distribution

*  Single-Variable Statistics

Examples with Complex Numbers

MODE 5:  CPLX

There are two separate registers to hold parts of complex numbers:

[ a ]:  Real part (rectangular),  Radius (polar)

[ b ]:  Imaginary part (rectangular), Angle (polar)

Example 1:  (4 + 3i) * (11 - 2i)

4 [ a ] 3 [ b ] [ × ] 11 [ a ] 2 [ +/- ] [ b ] [ = ]

Display:  50

Press [ b ], Display:  25

Result:  50 + 25i

Example 2:  Convert 3 + 2.4i to polar form, degrees

3 [ a ] 2.4 [ b ] [ INV ] (R>P)

Display:  3.841874542

Press [ b ],  Display:  38.65980826

3 + 2.4i = 3.841874542 ∠ 38.65980826°

Examples with Normal Distribution

MODE 6:  STAT

There are three functions that determine the area under the normal distribution curve:

P(t) from - ∞ to t,  lower tail curve

R(t) from 0 to t

Q(t) from t to ∞, upper tail curve

Note that for any t, P(t) + Q(t) = 1.

Also note that P(t), R(t), and Q(t) will operate on the standard normal curve, where μ = 0 and σ = 1, regardless of the amount of data points entered in Statistics mode through Σ+.

For z = t =2:

2 [ INV ] ( P(t) ) returns 0.97725

2 [ INV ] ( R(t) ) returns 0.47725

2 [ INV ] ( Q(t) ) returns 0.02275

Comparison:  TI-36 Solar vs. TI-35 Plus

The TI-36 Solar and TI-35 Plus have the same set of functions and features.  You can see my retro review from 2017 of the TI-35 Plus here:  http://edspi31415.blogspot.com/2017/09/retro-review-texas-instruments-ti-35.html

There are several keyboard differences:

Shift key is marked [ INV ] (with 2nd above it) for the TI-36 Solar, and the shift key is marked [ 2nd ] for the TI-35 Plus.

The equals key is twice in vertical height, covering the spans of the bottom two rows on the TI-35 Plus.

The top three rows* (all of the shift markings remain intact):

TI-36 Solar:

[CE/C] [ 1/x ] [ a ] [ b ] [ AC ]

[ hyp ] [ sin ] [ cos ] [ tan ] [ DRG ]

[ INV ] [ x^2 ] [ log ] [ ln x ] [ y^x ]

TI-35 Plus:

[ 2nd ] [ x^2 ] [ log ] [ ln x ] [ OFF ]

[ hyp ] [ sin ] [ cos ] [ tan ] [ DRG ]

[ y^x ] [ 1/x ] [ a ] [ b ] [ ÷ ]

The [ hyp ] key has the hyp^-1 label over it on the TI-35 Plus.

*not counting the [ON/C] key above all the rows on the TI-35 Plus

Comparison:  TI-36 Solar vs. the original TI-36X Solar

Here is my review from 2018 for the TI-36X Solar:  http://edspi31415.blogspot.com/2018/09/retro-review-texas-instruments-ti-36x.html

The TI-36X Solar:

*  does not have the complex arithmetic mode of the TI-36 Solar

*  adds the Boolean functions AND, OR, XOR, XNOR, and NOT to the BIN, OCT, and HEX mode

*  adds a second shift key, [ 3rd ]

*  there is no [ MODE ] key, every mode is selected through [ 3rd ] (key) combos

*  adds 8 scientific constants and 10 metric/US conversions

Verdict

Like the TI-35 Plus, the TI-36 Solar is a step up from the TI-30 series (1980s versions of TI-30).   Again, the TI-34 (1987) has the Boolean functions and fraction functions that the TI-36 Solar doesn't.  You don't have to worry about batteries at all since the TI-36 Solar runs entirely on solar/light power.

Eddie

All original content copyright, © 2011-2020.  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.

## Sunday, September 20, 2020

### Sumat 6

Sumat 6

Introduction

The Addimult Sumat 6 is a mathmatical aid designed to aid the user in addition and subtraction calculations.  Addimult was primarily based in Germany and Liechtenstein, which produced mechanical slides of allowing the user to add and subtract numbers of different amounts of digits (usually from 5 to 9).    Addimult produced sliders from the 1930s to the 1960s.

This summer, I found and purchased a Sumat 6 in antique shop in Manhattan Beach, California.  It was fortunate that the Sumat 6 came with a nice pouch, which was still intact and instructions.   It is a very classy machine which held up well for at least a 50 year old machine.

The Sumat 6 presented today has a six digit capacity.  The slider is made of metal and has two sides:

The Addition Side  (slider bar on top)

The Subtraction Side (slider bar on the bottom)

The Sumat 6, like all the mechanical slides produced at the time, has a metal stylus.  The stylus is used to push columns up and down in holes.  On top of each column has a circle that shows its value.  The markers in each column are either metallic silver or painted red.  For example, on the Addition side, a column that shows three red markers followed by seven silver markers gives the column a value of 3.   On the Subtraction side, a column that shows seven red markers followed by three silver markers shows a value of 3.

The value changes depending on what direction you push the slide:

Operation Slide Down Slide Up
Subtraction value decreases value increases

There are two additional markers, shown in red:  the up arrow and the down arrow.

Red Up Arrow ( ↑ ) : Push the next left column down 1.   Scroll the current column all the way up (0 on the Addition side, 9 on the Subtraction side)

Red Down Arrow ( ↓ ) : Push the column down one spot (to 0 on the Addition side, 9 on the Subtraction side)

Updating one column does not automatically update other columns, so you need to keep your addition and subtraction processes in your head as you are calculating.

Examples

Example 1:  425 + 784

Use the Addition side.   Set the sliders to 000425.

Start with the ones digit, which in this case is the right-most column.  Slide it down four notches.  So far, so good. Readout should have 000429.

Now the tens, slide the column down 8. Note that after 8 notches we hit the red up arrow.   Slide the hundred column down 1  and reset the tens column to 0.  You are done in the tens column since 8 notches are slid.  Readout should have 000509.

Finally the hundreds column, slide it down 7 notches.  Note after 5 notches, we hit the red up arrow again.   Time to slide the thousands column down 1 and reset the the hundreds column to 0.   We need to slide the hundreds column 2 more notches (5 of the 7 have been used).    The readout now has 001209.

The answer:  425 + 784 = 1209

Example 2:  1365 - 746

Use the Subtraction side.  Set the sliders to 001365.

In this problem the right-most column represent the ones digit.

Start with the ones digit and slide it down 6.  Note after six notches until the red up arrow is reached.   Slide the tens column down 1 and reset the ones column to 9.  Readout now should read 001359.

Now slide the tens column down 4.  Readout:  001319.

Now the hundreds, slide it down seven notches.  After four notches, the red up arrow is reached.   Slide down the thousands column and reset the hundreds column to 9.  We have three notches left, so slide the hundreds column down 3.  Readout:  000619.

We are done.

The answer:  1365 - 746 = 619

Sources

International Slide Rule Museum "Mechanical Slide & Rotary Adders" 2013-2018.  https://www.sliderulemuseum.com/Adders.htm   Retrieved September 5, 2020

Riches, David M.  "Addimult" Mathematical Instruments: A private collection.  August 2020.  http://www.mathsinstruments.me.uk/page25.html   Retrieved September 5, 2020.

Please visit or support the resources above!

Eddie

All original content copyright, © 2011-2020.  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.

## Saturday, September 19, 2020

### Casio fx-9750GIII: Beta Curve Fit

Casio fx-9750GIII:  Beta Curve Fit

The program BETAFIT will fit data to the curve

Y = A * x^B * (1-x)^C

Restrictions:  0 < x < 1 and y > 0

Derivation

General Equation:

Y = A * x^B * (1-x)^C

The equation can be transformed into a multilinear regression form by:

Y = A * x^B * (1-x)^C

ln Y = ln (A * x^B * (1-x)^C)

ln Y = ln A + ln (x^B) + ln (1-x)^C

ln Y = ln A + B * ln x + C * ln (1 - x)

y' = a' + b * x1 + c * x2

where:

y = ln Y

a = ln A,  A = e^a

x1 = ln x

x2 = ln(1 - x)

To find a Beta regression fit:

1.  Enter the x data.  Take two transformations:  ln x and ln(1 - x).   Recall 0 < x < 1.

2.  Enter the y data.  The the transformation ln y.  Recall y > 0.

3.  Execute multilinear regression: y' = a + b * x1 + c * x2.   See the notes above.

4.  Solve for the coefficients:

A = e^A

B = b

C = c

Matrix Setup:

X a = y

X Columns:  [ 1, ln x, ln(1 - x) ]

y Columns: [ ln y ]

Casio fx-9750GIII Program:  BETAFIT

Size: 300 Bytes

"2020-08-30 EWS"

"X DATA"? → List 1

"Y DATA"? → List 2

List 1 → List 3

Fill(1, List 3)

ln List 1 → List 4

ln (1 - List 1) → List 5

ln List 2 → List 6

List→Mat(List 3, List 4, List 5) → Mat B

List→Mat(List 6)→Mat C

(Trn Mat B × Mat B)^-1 × Trn Mat B × Mat C → Mat A

e^Mat A[1,1] → A

Mat A[2, 1] → B

Mat A[3, 1] → C

ClrText

Locate 1,3,"Y = A X^B (1-X)^C"

Locate 1,4,"A="

Locate 4,4,A

Locate 1,5,"B="

Locate 4,5,B

Locate 1,6,"C="

Locate 4,6,C

Examples

Graphs are not included in the program.

Example 1:

Data:

(0.1, 0.74)

(0.3, 0.7681)

(0.5, 0.55)

(0.7, 0.2779)

(0.9, 0.053)

A = 2.199360522

B = 0.3998640121

C = 1.599725605

Example 2:

Data:

(0.1, 0.015)

(0.3, 0.228)

(0.5, 1.24)

(0.7, 6.75)

(0.9, 100.44)

A = 1.261477517

B = 2.015236182

C = -1.992644053

Source:

Kolb, William M.  Curve Fitting For Programmable Calculators IMTEC.  Bowie, MD 20716.  1982.  ISBN-10:  0-943494-00-01

Stay safe and sane everyone.  Happy Birthday Press Your Luck (no whammies) Blessings,

Eddie

All original content copyright, © 2011-2020.  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.

## Tuesday, September 15, 2020

### New TI-Nspire CX/CX II Update

New TI-Nspire CX/CX II Update

Texas Instruments offers a software update:  5.2.   New to version 5.2:  Python.

Both the handheld software and computer software have the new update.

Eddie

All original content copyright, © 2011-2020.  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.

## Sunday, September 13, 2020

### Numworks: Generating a Colorful Matrix

Numworks:  Generating a Colorful Matrix

(updated 10/18/2021)

Introduction

Today's script generates a 3 x 3 matrix of random integers from 1 - 9 which each of the numbers are assigned a color.  The numbers are displayed in a 3 x 3 grid using the 320 x 240 pixel screen.

The colors which are assigned to each number are:

1:  Shamrock Green  (0, 158, 96)

2:  Denim Blue (21, 96, 189)

3:  Navy Blue (0, 0, 128)

4:  Indigo (75, 0, 130)

5:  Red (255, 0, 0)

6:  Rose (255, 0, 127)

7:  Brown (101, 67, 33)

8:  Orange (255, 127, 39)

9:  Gold (255, 223, 0)

Numworks Python Script:  colormtx.py

from math import *

from random import *

from kandinsky import *

# 2020-08-25 EWS

# color arrays

# red

mr = [ 0, 21, 0, 75, 255, 255, 101, 255, 255 ]

# green

mg = [ 158, 96, 0, 0, 0, 0, 67, 127, 223 ]

# blue

mb = [ 96, 189, 128, 130, 0, 127, 33, 39, 0 ]

# set up matrix

mat = [ [ 0, 0, 0 ], [ 0, 0, 0 ], [ 0, 0, 0 ] ]

# generate random numbers, assign colors

for r in range(3):

for c in range(3):

mat[ r ][ c ] = randint(1,9)

x = 80 + 80 * c

y = 60 + 60 * r

s = mat[ r ][ c ]

draw_string(str(s), x, y, color(mr[s-1], mg[s-1], mb[s-1]))

Gratitude to Brian who let me know about my typo on the last line, it was missing the final right parenthesis.

Remember that the index of arrays and matrices go from 0 to n-1.

Examples

Eddie

All original content copyright, © 2011-2020.  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.

## Saturday, September 12, 2020

### Casio fx-9750GIII: Happy Integers

Casio fx-9750GIII: Happy Integers

What Makes an Integer Happy?

1.  Take a positive integer

2.  Take the sum of the squares of its integers

3.  Repeat the process until:

a.   You repeat a previous result or

b.   You obtain a sum of 1.

In the cases that you eventually reach 1, that number is defined as a happy integer.

23:

2^2 + 3^2 = 13

1^2 + 3^2 = 10

1^2 + 0^2 = 1

23 is a happy integer.

24:

2^2 + 2^2 = 4

4^2 = 16

1^2 + 6^2 = 37

3^2 + 7^2 = 58

5^2 + 8^2 = 89

8^2 + 9^2 = 145

1^2 + 4^2 + 5^2 = 42

4^2 + 2^2 = 20

2^2 + 0^2 = 4    (see first addition - repeat)

24 is not a happy integer.

The sequence of sums of squares of the integer's digits is known as a cherry sequence.

Casio fx-9750GIII: HAPPY

(316 bytes)

"2020-08-20 EWS"

"N>0, INTEGER: N"? → N

{ 0 } → List 1

Intg log N → D

N ÷ 10^D → W

Lbl 3

0 → T

For 0 → I To D

T + (Intg W)^2 → T

(W - Intg W) × 10 → W

Next

Augment(List 1, { T }) → List 1

ClrText

Locate 1, 4, T

For 1 → I To 100

Next

T = 1 ⇒ Goto 1

For 1 → I To Dim List 1 - 1

T = List 1[ I ] ⇒ Goto 2

Next

T → W

Intg log W → D

W ÷ 10^D → W

Goto 3

Lbl 1

ClrText

Locate 1, 3, W

Locate 1, 4,"IS A HAPPY INTEGER"

Stop

Lbl 2

Locate 1, 3, N

Locate 1, 4, "NOT A HAPPY INTEGER"

Stop

Notes:

(1)  10^ is shown as a subscript 10 on the calculator.

(2)  The program sequence

ClrText

Locate 1, 4, T

For 1 → I To 100

Next

creates a timer.  This allows the calculator to show intermediate results for a short time.

(3)  Intermediate sums of squares are stored in List 1.  Other than the first 0 (an element is required to start a list in Casio programming), the rest of the sequence is known as Cheery Sequence.

Examples

N = 19;  Happy Number

N = 77; Not a Happy Number

N = 230; Happy Number

N = 562; Not a Happy Number

Sources:

Duncan, Donald C.  Happy Integers.  The Mathematics Teacher, Vol 65. No. 7  November 1972, pp. 627-629  https://www.jstor.org/stable/27959021

Happy Number.  GeeksforGreeks.  https://www.geeksforgreeks.org/happy-number  Updated February 4, 2020.  Accessed August 19, 2020.  (website under maintenance)

Eddie

All original content copyright, © 2011-2020.  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.

## Sunday, September 6, 2020

### Retro Review: Sharp EL-512 Scientific Calculator

Retro Review: Sharp EL-512 Scientific Calculator

Just The Facts:

Model:  EL-512
Company: Sharp
Type:  Keystroke Programmable
Display:  10 digits, 8 digits with 2 digit exponents
Battery:  Battery: 2 x LR 44
Logic: AOS
Memory Registers: 10; 9 with an M registers.
Programming Memory: 128 steps

Years:  1984-1987

Basic Information:

The manual can be found here:

Features

* Trigonometric, Hyperbolic, Logarithmic, and Exponential Functions
* Constant Arithmetic
* Automatic Multiplication
* Convert to Degrees-Minutes-Seconds
* Linear Regression

Constant Arithmetic

Pressing the equals key after a completed arithmetic operation will put the EL-512 into automatic arithmetic mode. This works only for addition, subtraction, and multiplication.

Keystrokes Interpretation Examples
A [ + ] B [ = ]
C [ = ]
D [ = ]
A + B
C + B
D + B
150 [ + ] 80 [ = ] 230
76 [ = ] 156
52 [+/-] [ = ] 28
A [ - ] B [ = ]
C [ = ]
D [ = ]
A - B
C - B
D - B
150 [ - ] 80 [ = ] 70
76 [ = ] -4
52 [+/-] [ = ] -132
A [ × ] B [ = ]
C [ = ]
D [ = ]
A × B
C × B
D × B
20 [ × ] 4 [ = ] 80
5 [ = ] 100
0.25 [ = ] 5

Automatic Multiplication

Automatic (implied) multiplication occur in several areas:

The Famous A / BC Problem:

A [ ÷ ] B [ ( ] C [ ) ] [ = ]   returns A / (B * C)
Example:  9 [ ÷ ] 3 [ ( ] 2 [ ) ] [ = ]  returns 1.5

A [ ÷ ] B [ × ] C [ = ]   returns A / B * C
Example:  9 [ ÷ ] 3 [ × ] 2 [ = ] returns 6
.
Multiply by π:

A [ π ] returns A * π automatically.
Example:  5 [ π ] returns 15.70796327

Implied Multiplication with Stored Numbers

With a stored number in a number register Kn:
A [ Kn ] returns A * Kn automatically
Example:  11.5 [ 2ndF ] (STO) 1;   5 [ Kn ] 1 returns 57.5

This is a very neat shortcut in keystroke programming.

The sequence [ 2ndF ] ( →HEX ) converts the number to hexadecimal form and changes the EL-512 to Hexadecimal mode.  Enter the digits A - F, by pressing [ 2ndF ] [ 0 ], [ 2ndF ] [ 1 ], etc.   I like the placement of A - F since A = 10, B = 11, etc.   Pressing the equals key returns the EL-512 to Decimal mode.

Unfortunately no Boolean functions are offered.

Linear Regression

The memory keys act as data point entry.  In this mode, the multiplication key is used to indicate frequency.  The linear regression line is y = a + bx, where a is the intercept and b is the slope.

Programming

The programming model for the EL-512 is algebraic keystroke, which the manual refers to as Multiple Formula Reserve.  Programs are entered "blindly" so make sure that you have the program written down before entering it.

You will also need to enter the program as a test case.

The program space is 128 steps between 4 program spaces.  Every time a new program is entered, the old program in that slot is automatically cleared.  The LRN indicator shows that the EL-512 is in learn mode.

[ x ]:  Asks the user to enter number.  Prompt numbers start with 1 and increases by 1.  This does not affect any storage registers.  Numbers entered after the [ x ] during program do not count as steps.   In run mode, enter the number, then press [ COMP ].

[ 2ndF ] (LOOK):  This allows the program to temporarily stop to show the displayed value.  Continue the program in run mode by pressing [COMP].

[ 1: ], [ 2: ], [ 2ndF ] ( 3: ), [ 2ndF ] ( 4: ):  In run mode, these keys and key sequences runs the program slot.

There are no loops, integer, fraction, sign functions, or comparisons. Hence this model's programming is strictly for formulas only.

Sharp EL-512 Program:  Rating Microphones in dBm

dBm = 10 log ( (E^2) / (0.001 * Z)) - 6

E:  voltage, prompt [ 1 ]
Z:  resistance (ohms), prompt [ 2 ]

Program:

[ x ]
(enter E)
x^2
÷
0.001
÷
[ x ]
(enter Z)
=
log
×
10
-
=

Examples:

E = 40, Z = 80, Result:  37.01029996
E = 70, Z = 100, Result:  40.9019608

Source:
Davis, Don and Davis, Carolyn.  Sound System Engineering.  Howard W. Sams & Co. Inc:  Indianapolis.  1975  ISBN-10:  0-672-21156-4

Sharp EL-512 Program:  Heron's Formula

Area = √(S * (S - A) * (S - B) * (S - C)) where S = (A + B + C) / 2

A:  length of side A, prompt [ 1 ]
B:  length of side B, prompt [ 2 ]
C:  length of side C, prompt [ 3 ]

Program:

[ x ]
(enter A)
STO 1
+
[ x ]
(enter B)
STO 2
+
[ x ]
(enter C)
STO 3
=
÷
2
=
STO 4
×
Kn 4
Kn 1
)
×
(
Kn 4
-
Kn 2
×
(
Kn 4
-
Kn 3
=

Examples:
A = 15.6, B = 13.8 , C = 14.8;  Area: 93.29390923
A = 48, B = 42, C = 57; Area:  986.9860371

Verdict

I think the most unique feature to the EL-512 is the implied multiplication.   I wish the programming functions had integer and fraction functions and even some comparisons.  The calculator is small and compact and fits very nicely in the wallet.   The keys, even though they are small to me, are nice and responsive.

Eddie

All original content copyright, © 2011-2020.  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.

## Saturday, September 5, 2020

### Casio fx-9750GIII: Combination Matrices

Casio fx-9750GIII:  Combination Matrices

Introduction

The program COMBMTRX creates an aligned combination triangle with rows 0 to W-1 and columns 0 to W-1.  The matrix is a square matrix with size W x W.

1.  Pascal

n NCR k

2.  Catalan

(n - k + 1) / (n + 1) * [ n+k NCR n ]

3.  Borel

1 / (n + 1) * [ 2n+2 NCR n-k ] * [ n+k NCR n ]

4.  User Function

f(n, k,  h(n,k) NCR g(n,k))

"Blank" spaces will be filled with 0.

Casio fx-9750GIII Program:  COMBMTRX

(320 bytes)

Note:  On the program screen, nCr will be symbolized as a bold C

"2020-08-11 EWS"

"COMBINATION MATRIX"

"SIZE"? → W

Identity W → Mat A

Lbl 1

"(N)nCr(K)" → fn1

Goto 5

Lbl 2

"(N-K+1)÷(N+1)×(N+K)nCr(N)" → fn1

Goto 5

Lbl 3

"1÷(N+1)×(2N+2)nCr(N-K)×(N+K)nCr(N)" → fn1

Goto 5

Lbl 4

"F(N,K)"? → fn1

Goto 5

Lbl 5

For 1 → I To W

For 1 → J To I

I-1 → N

J-1 → K

fn1 → Mat A[I,J]

Next

Next

Mat A

Examples

Size: 5

Option 1:  Pascal

[[ 1 0 0 0 0 ]

[ 1 1 0 0 0 ]

[ 1 2 1 0 0 ]

[ 1 3 3 1 0 ]

[ 1 4 6 4 1 ]]

Option 2:  Catalan

[[ 1 0 0 0 0 ]

[ 1 1 0 0 0 ]

[ 1 2 2 0 0 ]

[ 1 3 5 5 0 ]

[ 1 4 9 14 14 ]]

Option 3:  Borel

[[ 1 0 0 0 0 ]

[ 2 1 0 0 0 ]

[ 5 6 2 0 0 ]

[ 14 28 20 5 0 ]

[ 42 120 135 70 14 ]]

Option 4:  User

f = (N+K+1)nCr(K) ÷ (N=1)

(in fraction form)

[[ 1 0 0 0 0 ]

[ 1/2 3/2 0 0 0 ]

[ 1/3 4/3 10/3 0 0 ]

[ 1/4 5/4 15/4 35/4 0 ]

[ 1/5 6/5 21/5 56/5 126/5 ]]

Source:

Cai, Yue and Yan, Catherine.  "Coutning with Borel's Triangle"  Elsevier B.V. Discrete Mathematics.   November 15, 2018  https://arxiv.org/pdf/1804.01597.pdf

Retrieved August 9, 2020

Eddie

All original content copyright, © 2011-2020.  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.

### HP 15C: Error Function and Lower Tail Normal Cumulative Function

HP 15C:   Error Function and Lower Tail Normal Cumulative Function Formulas Used  Error Function  erf(x) = 2 ÷ √π * ∫( e^(-t^2) dt, t = 0 t...