Wednesday, April 18, 2018

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



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.

Monday, April 16, 2018

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.

Thursday, April 12, 2018

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.

Wednesday, April 11, 2018

April 11, 2018: Seven Years


April 11, 2018:  Seven Years

The blog is officially 7 years old! I love mathematics and this blog has one way of expressing that passion. 

It wouldn’t be the success that it is without you, your comments, and your support. Thank you so much‼!

By the way, I also added a file below, which is a collection of some mathematical formulas and refines including:

* Geometry
* Trigonometry
* Basic Finance
* Calculus
* Differential Equations
* Statistics – Linear Regression
* Quadratic and Cubic Equations
* Constants and Solar System Data


Why did I use a large font?  My aim is to create a reference that would fit and be readable, even on Android or iPhone smartphones.  This is a quick reference that can be used off line.  If you download the PDF file, I hope you enjoy this and find it helpful.

Here’s to another year!

Eddie

Review: Canon F-730SX Calculator

Review:  Canon F-730SX Calculator General Information Company:  Canon Type:  Scientific Memory:  5 Registers A, B, C, D, E ...