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Casio fx-115ES Plus
09-08-2014, 02:00 PM (This post was last modified: 09-08-2014 02:28 PM by Don Shepherd.)
Post: #1
Casio fx-115ES Plus
For a calculator that costs less than $20, this unit has some very interesting features, including:

  1. Sigma and Product functions
  2. Simplifies fractions
  3. Simplifies square roots (normally found only on CAS calculators)
  4. Finds prime factors (limited to factors up to 3 digits)
  5. Equation solver
  6. Reference last answer and the one before that!
  7. Solves inequalities
  8. Repeating decimals


The repeating decimals feature is particularly interesting. I entered a calculation that resulted in the fraction 385/1608. I pressed the key to get the decimal equivalent and it showed 0.239427860696517412935323383084577114 with a vinculum bar above the digits starting at 427. Amazing.
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09-08-2014, 03:13 PM
Post: #2
RE: Casio fx-115ES Plus
It is rather amazing what you get for $20. Sharp also has a model with similar capabilities, the EL-W516.

There is a good comparison between the SHARP EL-W516 and the CASIO fx-115ES calculators at:
http://members.bex.net/jtcullen515/Math8.htm

More than a simple comparison, the two volumes presented here (175 pages) are also a good tutorial on how to use these models. The information is usable for newer Casio and Sharp scientific calculator models as well.
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09-09-2014, 04:34 AM
Post: #3
RE: Casio fx-115ES Plus
It also does numerical integration, BIN OCTAL HEX arithmetic, and the Plus added an integer function so you can calculate the remainder, though a MOD function would have been better. Still, I agree it's quite impressive for less than $20.
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09-09-2014, 10:42 PM (This post was last modified: 09-09-2014 10:43 PM by SlideRule.)
Post: #4
RE: Casio fx-115ES Plus
I purchased mine for under $12 at _-_art (blanked on purpose). I use it as my calculator of first choice for my Technical Mathematics classes. I'm a long-time HP fan, going ALL the way back to the 65 BUT this Casio outperforms my prior choice calculator, the HP-300s+. Like the WP-31S I recently purchased, I don't need programming with the level of SOLVE and the depth of FUNCTIONS provided on the 115ES+.

BEST!

SlideRule
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09-11-2014, 11:54 PM (This post was last modified: 09-12-2014 03:05 AM by Joe Horn.)
Post: #5
RE: Casio fx-115ES Plus
(09-09-2014 10:42 PM)SlideRule Wrote:  I purchased mine for under $12 at _-_art (blanked on purpose).

Today I bought one there also, for $12.97, no shipping charges because they are nearby. The "recurring decimal" functionality is sweet; I've never seen it on a calculator before.

EDIT: corrected "fraction" to "decimal".

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09-12-2014, 12:51 AM
Post: #6
RE: Casio fx-115ES Plus
Here is a Youtube video featuring this calculator, and the presenter shows several ways to use this calc with students so that they can discover the rules for certain math concepts on their own instead of just hearing the teacher say "this is the rule." Toward the end of the video he also shows how to use the Preanswer and Answer functions to easily generate the Fibonacci sequence. Very cool.
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09-12-2014, 03:31 AM (This post was last modified: 09-12-2014 03:50 AM by Gerson W. Barbosa.)
Post: #7
RE: Casio fx-115ES Plus
(09-12-2014 12:51 AM)Don Shepherd Wrote:  Toward the end of the video he also shows how to use the Preanswer and Answer functions to easily generate the Fibonacci sequence. Very cool.

Easier than 1 ENTER + g LSTx x<>y + g LSTx x<>y +... ?

P.S.: Or, on the WP 34S,

1 ENTER +
RCL+ L
RCL+ L
...
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09-12-2014, 08:41 AM
Post: #8
RE: Casio fx-115ES Plus
(09-12-2014 03:31 AM)Gerson W. Barbosa Wrote:  1 ENTER +
RCL+ L
RCL+ L
...

(04-18-2014 05:24 PM)Thomas Klemm Wrote:  I like to hit a key repeatedly and look what happens:
Quote:Try this during a boring lecture: Set your calculator to radians mode and then repeatedly press the cos button until you obtain the fixed point.
Structure and Interpretation of Computer Programs
Footnote 57

With the HP-48 you can use:
Code:
\<< SWAP OVER + \>>
LUCAS
STO

0 1
LUCAS
LUCAS
LUCAS
...

Code:
\<< OVER SWAP * \>>
FIBO
STO

[[1 1]1 0] [1 0]
FIBO
FIBO
FIBO
...


Cheers
Thomas
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09-12-2014, 08:54 AM
Post: #9
RE: Casio fx-115ES Plus
(09-12-2014 03:31 AM)Gerson W. Barbosa Wrote:  
(09-12-2014 12:51 AM)Don Shepherd Wrote:  Toward the end of the video he also shows how to use the Preanswer and Answer functions to easily generate the Fibonacci sequence. Very cool.

Easier than 1 ENTER + g LSTx x<>y + g LSTx x<>y +... ?

P.S.: Or, on the WP 34S,

1 ENTER +
RCL+ L
RCL+ L
...
About the same:

1 = = preanswer + answer = ...

but on a non-programmable $13 calculator!
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09-12-2014, 02:11 PM
Post: #10
RE: Casio fx-115ES Plus
(09-12-2014 08:41 AM)Thomas Klemm Wrote:  
(09-12-2014 03:31 AM)Gerson W. Barbosa Wrote:  1 ENTER +
RCL+ L
RCL+ L
...

With the HP-48 you can use:
Code:
\<< SWAP OVER + \>>
LUCAS
STO

0 1
LUCAS
LUCAS
LUCAS
...

Code:
\<< OVER SWAP * \>>
FIBO
STO

[[1 1]1 0] [1 0]
FIBO
FIBO
FIBO
...

On the WP 34S:

Code:

001 LBL A
002 0
003 INC X
004 FIB
005 PSE 10
006 x<> L
007 BACK 004
008 END

or

Code:

001 LBL A
002 0
003 x!
004 PSE 10
005 RCL+ L
006 BACK 002
007 END

Cheers,

Gerson.
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09-12-2014, 02:14 PM (This post was last modified: 09-12-2014 02:14 PM by Gerson W. Barbosa.)
Post: #11
RE: Casio fx-115ES Plus
(09-12-2014 08:54 AM)Don Shepherd Wrote:  
(09-12-2014 03:31 AM)Gerson W. Barbosa Wrote:  Easier than 1 ENTER + g LSTx x<>y + g LSTx x<>y +... ?

P.S.: Or, on the WP 34S,

1 ENTER +
RCL+ L
RCL+ L
...
About the same:

1 = = preanswer + answer = ...

but on a non-programmable $13 calculator!

Nice! The only thing I dislike is prime factors being limited to 3 digits.
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09-12-2014, 03:24 PM
Post: #12
RE: Casio fx-115ES Plus
Quote:Nice! The only thing I dislike is prime factors being limited to 3 digits.

Yeah, I'm not a big fan of that either, but this is a non-CAS $13 system after all.

I think the repeating decimals function is the major feature of this guy.

The Youtube video I mentioned in one post is very good, I am considering whether to use this calc with the students in my algebra class. I have not used any calculators in the last few years in my classes, but I very much like the idea of "let the students experiment and figure out the rule without me saying what the rule is".
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09-13-2014, 03:10 AM
Post: #13
RE: Casio fx-115ES Plus
(09-12-2014 08:54 AM)Don Shepherd Wrote:  
(09-12-2014 03:31 AM)Gerson W. Barbosa Wrote:  Easier than 1 ENTER + g LSTx x<>y + g LSTx x<>y +... ?

P.S.: Or, on the WP 34S,

1 ENTER +
RCL+ L
RCL+ L
...
About the same:

1 = = preanswer + answer = ...

but on a non-programmable $13 calculator!

Various methods for various machines have been posted in this thread, but the Casio wins the "keystroke efficiency" competition (at least after a few iterations). As Don shows above, the Fibonacci Sequence has a 7 keystroke setup (including one shift key), and each iteration takes only 1 keystroke. Other sequences are similar:

Pell Sequence:
Setup: 0, =, 1, =, 2, Ans, +, ALPHA, PreAns (9 keystrokes)
Iterate: = (1 keystroke)
--> 2, 5, 12, 29, 70, 169, ... (up to the 32nd Pell number, after which it flips into scientific notation and loses digits).

Also, Casio has long supported multiple statements in one line (separated by a colon), which lets you execute an entire sequence of commands repeatedly, by simply by pressing the = key repeatedly. Very cool. Do any non-Casio algebraic calculators do this?

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09-13-2014, 10:06 AM
Post: #14
RE: Casio fx-115ES Plus
(09-13-2014 03:10 AM)Joe Horn Wrote:  Also, Casio has long supported multiple statements in one line (separated by a colon), which lets you execute an entire sequence of commands repeatedly, by simply by pressing the = key repeatedly.
Does this mean that the following can be used to calculate \(\pi\)?

0 =
2 =
√ PreAns + 2 : 2 PreAns / Ans =
=
...

As I didn't consult the manual some parentheses might be missing.

Quote:Very cool.
Yes, indeed.

Cheers
Thomas
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09-13-2014, 11:11 AM (This post was last modified: 09-13-2014 12:22 PM by Don Shepherd.)
Post: #15
RE: Casio fx-115ES Plus
Quote:Does this mean that the following can be used to calculate \(\pi\)?

0 =
2 =
√ PreAns + 2 : 2 PreAns / Ans =
=
...

Yes, Thomas, that yields 3.141592654 after 33 iterations.
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09-13-2014, 01:51 PM
Post: #16
RE: Casio fx-115ES Plus
(09-13-2014 11:11 AM)Don Shepherd Wrote:  
Quote:Does this mean that the following can be used to calculate \(\pi\)?

0 =
2 =
√ PreAns + 2 : 2 PreAns / Ans =
=
...

Yes, Thomas, that yields 3.141592654 after 33 iterations.

Very cool! And Thomas's having got it right without either calculator or manual was just über-cool!
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09-13-2014, 04:32 PM
Post: #17
RE: Casio fx-115ES Plus
TI-57:

CLR 1 x<>t 0
x<>t +
x<>t +
x<>t +
...
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09-14-2014, 01:45 PM
Post: #18
RE: Casio fx-115ES Plus
(09-13-2014 11:11 AM)Don Shepherd Wrote:  Yes, Thomas, that yields 3.141592654 after 33 iterations.

Don, thanks for taking the time to confirm this. What bothers me a little is that it needs 33 iterations since that's what I get when the result is rounded to 10 significant digits:

Code:
      PreAns        Ans
 0:   0.000000000   2.000000000
 1:   1.414213562   2.828427125
 2:   1.847759065   3.061467459
 3:   1.961570561   3.121445152
 4:   1.990369453   3.136548491
 5:   1.997590912   3.140331157
 6:   1.999397637   3.141277251
 7:   1.999849404   3.141513801
 8:   1.999962351   3.141572940
 9:   1.999990588   3.141587725
10:   1.999997647   3.141591422
11:   1.999999412   3.141592346
12:   1.999999853   3.141592577
13:   1.999999963   3.141592634
14:   1.999999991   3.141592649
15:   1.999999998   3.141592652
16:   1.999999999   3.141592653
17:   2.000000000   3.141592654
18:   2.000000000   3.141592654
19:   2.000000000   3.141592654
20:   2.000000000   3.141592654
21:   2.000000000   3.141592654
22:   2.000000000   3.141592654
23:   2.000000000   3.141592654
24:   2.000000000   3.141592654
25:   2.000000000   3.141592654
26:   2.000000000   3.141592654
27:   2.000000000   3.141592654
28:   2.000000000   3.141592654
29:   2.000000000   3.141592654
30:   2.000000000   3.141592654
31:   2.000000000   3.141592654
32:   2.000000000   3.141592654
33:   2.000000000   3.141592654

Where does it start to deviate?

Cheers
Thomas
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09-14-2014, 05:39 PM (This post was last modified: 09-14-2014 05:48 PM by Don Shepherd.)
Post: #19
RE: Casio fx-115ES Plus
Quote:Where does it start to deviate?

My mistake, I was counting each press of the = key as an iteration and counting the keypresses until it showed 3.141592654. Each = key press executes expressions between colons. So it is actually 16 I think.

I get exactly what you get.
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09-14-2014, 07:57 PM
Post: #20
RE: Casio fx-115ES Plus
(09-14-2014 05:39 PM)Don Shepherd Wrote:  So it is actually 16 I think.

That makes more sense. For k correct digits of \(\pi\) you need about k/log10(4) ~ 1.66k iterations.
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