Scientific Calculator Basics Document Now Available

Scientific Calculator Basics Document Now Available

If you are new to scientific calculators, ever wondered what the [sin], [log], and [e^x] keys actually mean, or want a refresher on the basics: then this tutorial is for you.

The document convers common scientific functions such as:

* Typing in large and small numbers by using scientific notation

* Calculating powers and roots

* Logarithms and anti-logarithm functions

* Trigonometric functions, such as sine, cosine, and tangent; along with their inverses

* Basic statistic and linear regression calculations

* How to enter fractions and numbers in degrees-minutes-seconds formats

* How to convert integers between binary, octal, decimal, and hexadecimal

This document covers a variety of scientific calculators, aimed at infix algebraic (two or multi-line scientific) calculators.

Download Scientific Calculator Basics (Infix Algebraic Notation) Here

Eddie

All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions.

Review: Canon F-730SX Calculator

Review:  Canon F-730SX Calculator

General Information

Company:  Canon

Type:  Scientific

Memory:  5 Registers A, B, C, D, E

Battery:  Solar with battery back up (LR 44)

Years:  2017 - present

Original Cost: retail price is currently $13.95

Operating System:  Algebraic, Infix notation

Product Page:  https://www.usa.canon.com/internet/portal/us/home/products/details/calculators/scientific-calculators/f-730sx

Features

This Canon F-730SX calculator is a two-line display scientific calculator which offers a basic array of functions:  trigonometry, logarithms, exponents, polar and rectangular conversions, degrees and degrees-minutes-seconds conversions, and fraction calculations.  The F-730SX has base conversions functions and Boolean functions AND, OR, XOR, and XNOR available only in Binary, Octal, and Hexadecimal modes.  The Decimal mode works both for decimal integers and normal computation mode. 

The F-730SX offers 1 and 2 variable statistics, along with linear regression using the regression equation y = a + b*x.

The F-730SX has a two line display, the top line where you enter your expressions and the bottom line is where the results of all calculations are displayed. 

So this is a clone of the TI-30X IIS then?

Left: Texas Instruments TI-30X IIS, Right: Canon F-730SX

Not quite?  If you look at the picture above, they both look very similar.  However, there are few differences, most noticeable that the F-730SX has base conversions while the TI-30 XIIs doesn’t, and I also think the display is a bit larger on the F-730SX. 

Here is a breakdown of some of the features for both calculators:

Texas Instruments TI-30X IIS	Canon F-730SX
Display: 2 lines:  11 character top line; 10 digit accuracy	Display: 2 lines: 11 character top line; 10 digit accuracy; larger display
Expressions can hold up to 88 characters (47 in Statistics mode)	Expressions can hold up to 87 characters (47 in Statistics mode)
Angle indicator (DEG/RAD/GRAD) is on the right side of the screen	Angle indicator (DEG/RAD/GRAD) is on the left side of the screen
5 Memory Registers: A, B, C, D, E	5 Memory Registers: A, B, C, D, E
K constant operation	K constant operation
Random numbers and integers	Random numbers and integers
Linear Regression	Linear Regression
No Base Conversions or Boolean operations	Base Conversions (BIN/OCT/DEC/HEX) and Boolean operations (NOT, AND, OR, XOR, XNOR)
Backup battery:  CR2025, must take the entire back compartment off	Backup battery: LR44, has a small battery slot

My only real gripe with both of these calculators is on how memory is accessed.  The variables are menu based, hence it takes extra keystrokes to access variables B, C, D, and E than it would with installing an ALPHA key.  The speed of both calculators are comparable.

Verdict

The reasons why I would recommend a Canon F-730SX are these:  the F-730SX is usually sold at a lower price than the TI-30X IIs, and you get base conversions.  I would also argue that the screen is nicer, but the difference is not great, since the screen of the TI-30X IIs is still readable.  In Southern California (and maybe the United States), the F-730SX is currently sold at Fry’s, or you can get this calculator online too.

Eddie

All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions.

Combinatorics Derivations

Combinatorics Derivations

The definition of the combination function is:

C(n, r) = n! / (r! *  (n – r)!)

Today I am going to mathematically verify three equivalents in combinatorics.

Newton’s Identity

C(n,r) * C(r,k) = C(n,k) * C(n – k, r – k)

Here I am going to assume that n > r > k.

Hence:

C(n, r) * C(r, k)

= n! / (r! * (n – r)!) * r! / (k! * (r – k)!)

= n! / (n – r)! * 1 /  (k! * (r – k)!)

Rearrange:

= n! / k! * 1 / ((n – r)! * (r – k)!)

Multiply by (n – k)!/(n- k)!:

= n! / (k! * (n – k)!) * (n – k)! / ((n – r)! * (r – k)!)

Observe that (n – k) – (r – k) = n – k – r + k = n – r.  Hence,

= C(n,k) * C(n – k, r – k)   QED

Pascal’s Identity

C(n,r) = C(n-1, r) + C(n – 1, r – 1)

I’m going to start with C(n-1, r) + C(n – 1, r – 1)

C(n-1, r) + C(n – 1, r – 1)

= (n – 1)! / (r! * (n – 1 – r)!) + (n – 1)! / ((r – 1)! * (n – r)!)

= (n – 1)! / (r! * (n – 1- r)!) + (r * (n – 1)!) / (r! *(n – r)!)

= ((n – 1)! * (n – r)) / (r! * (n – r)!) + (r * (n – 1)!) / (r! * (n – r)!)

= (n * (n – 1)! – r * (n – 1)! + r * (n – 1)!) / (r! * (n – r)!))

= (n * (n  - 1)!) / (r! * (n – r)!)

= n! / (r! * (n – r)!)

= C(n, r)  QED

Combinatorial Proof

C(m + n, 2) – C(m, 2) – C(n, 2) = m * n

C(m + n, 2) – C(m, 2) – C(n, 2)

Note that 2! = 2

= (m + n)! / (2 * (m + n – 2)!) – m! / (2 * (m – 2)!) – n! / (2 * (n – 2)!)

= ( (m + n)! * (m – 2)! * (n – 2)! – m! * (m + n – 2)! * (n – 2)!  - n! * (m – 2)! * (m + n – 2)!) / (2 * (m + n – 2)! * (m – 2)! * (n – 2)!)

= ( (m + n) * (m + n – 1) *(m + n – 2)! * (m – 2)! * (n – 2)! – m * (m – 1) *(m – 2)! * (n – 2)! * (m + n – 2)! – n * (n – 1) * (n – 2)! * (m – 2)! * (m + n – 2)! )

/  (2 * (m + n – 2)! * (m – 2)! * (n – 2)!)

= ( (m + n)*(m + n – 1) – m * (m – 1) – n * (n – 1) ) / 2

= ( m^2 + m*n – m + m*n + n^2 – n – m^2 + m – n^2 + n) / 2

= (2 * m * n) / 2

= m * n   QED

Eddie

Source where I got the identities from:

V.K. Balakrishnan Schaum’s Theory and Problems: Combinatorics including concepts of Graph Theory  McGraw-Hill, Inc. New York: 1995  ISBN 0-07-003575-X

The derivation and proof details are my work.  

All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions.

HP Prime, HP 41C, TI-58C: Round to the Nearest 1/n

HP Prime, HP 41C, TI-58C:  Round to the Nearest 1/n

Introduction

The program RNEAR rounds a number x to the nearest 1/n.  For example, to round x to the nearest 10th, n = 10.  To round to the nearest 16th, n = 16.

HP Prime Program RNEAR

EXPORT RNEAR(x,n)

BEGIN

// round x to the nearest nth

// 2018-04-07 EWS

RETURN ROUND(FP(x)*n,0)/n+IP(x);

END;

HP 41C and Swiss Micros SM41 Program RNEAR

Keystrokes:  x [ENTER] y [XEQ] [ALPHA] RNEAR [ALPHA]

01 LBL^T REAR

02 FIX 0

03 STO 01

04 X<>Y

05 STO 02

06 RFC

07 *

08 RND

09 RCL 01

10 /

11 RCL 02

12 INT

13 +

14 FIX 4

15 RTN

TI-58C/TI-59 Program RNEAR

Store x into register 01

Store n into register 02

The result is stored in register 03

Minimum Registers Needed: 4 (I always leave register 00 for general use)

There is no rounding function on the TI-58C and TI-59, hence the rounding routine needs to be manually entered.

Step	Key Code	Key	Notes
000	43	RCL
001	01	01
002	22	INV
003	59	Int	INV Int: Frac
004	65	*
005	43	RCL
006	02	02
007	95	=
008	42	STO
009	03	03
010	00	0
011	93	.
012	05	5
013	32	x<>t	Store 0.5 to t
014	43	RCL
015	03	03
016	22	INV
017	59	Int
018	77	x≥t
019	55	[÷]	If frac(R03)≥0.5, go to label “÷”
020	76	Lbl
021	65	[*]	Label “×”
022	43	RCL
023	03	03
024	59	Int
025	55	÷
026	43	RCL
027	02	02
028	85	+
029	43	RCL
030	01	01
031	59	Int
032	95	=
033	42	STO
034	03	03
035	91	R/S	Display result
036	81	RST	End program
037	76	Lbl
038	55	[÷]	Label “÷”
039	01	1
040	44	SUM
041	03	03
042	61	GTO
043	65	[*]

Examples:

x = π

n = 10, result:  3.10 (nearest 10th)

n = 1000, result: 3.142 (nearest 1000th)

n = 16, result:  3.125 (nearest 16th)

Eddie

All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions.