(2012-11-27) Advanced calculators assign more than one function to most keys.
On the keyboards of basic calculators, every key is assigned one andonly one use, digit entry, binary operation (plus, minus, multiply or divide) orunary operation (typically, only the square root function is provided onsuch calculators).
Scientific calculators have to provide so many functionsthat several uses must be assigned to a single key. On the HP 35s, the additional functionalities are obtained by pressingeither of two special colored keys (blu or yellow) before punching the main key (whose extra functionality may beindicated by a label of the same color, either on the key itself or nearbyon the faceplate).
(2015-12-09) (Jan Lukasiewicz, 1924) RPN is the fastest way to enter data. Parentheses not needed.
(2012-11-27) Just the most common ones...
(2012-11-27) (e ) Accessible via one single menu selection.
HP advertises 41 physical constants, but their 41-st is the value of themathematical constante, the base of natural logarithms (2.718281828)... although it's otherwise readily available in 2½ keystrokes:
[ 1 ]
This is rather unfortunate, because the symbol e in any list of physical constants always refers to the elementary charge (the electric charge of a proton, the opposite of the charge of an electron). Since the value of the elementary charge in coulombs (C, the SI unit) is unavoidable in such a list, they skirted the issue by giving the value of theelectronvolt (eV) in joules (J) which is the samenumber (by the very definition of the electronvolt).
The molar volume given in the HP 35s is foranideal gas under co-called normal temperature and pressure (NTP, 0°C, 1 atm = 101325 Pa). In Casio calculators competing directly against the HP 35s, standard temperature and pressure (NTP, 0°C, 1 bar = 100000 Pa) is used instead to define that particular constant. Otherwise, the calculators of both manufacturers feature exactly the same set of 40 physical constants...
The built-in physical constants of the HP 35s are based on :
As of 2012, the above values have not been updated in the HP-35s since its first release, in 2007. They are based on on which was already several years out of date in 2007 ( was then current, since was only officialized in 2008). At this writing,the values listed above () have been current since June 2011and are not expected to be updated until 2015 or so.
The values highlighted in yellow correspond to slight mistakes and inaccuraciesin the HP 35s built-in constants. The constants singled-out in this way are known exactly (because of the way SI units are defined) but have beenrounded incorrectly and/or needlessly truncatedbelow the nominal 12-digit precision of the calculator (to say nothing of its advertised 15-digit precision for "internal computations").
Arnold Sommerfeld'sFine-Structureconstant () is the only listedconstant to be dimensionless. Its numerical value would be the samein any coherent system of physical units and it remains a mystery:
= 0c e2/ 2h = e2/ 2hc0 = 1 / 137.035999...
The following lengths form a geometric progression of common ratio :
1 / 2R 2a0c 2 re
That's the first of many noteworthy relations between the above constants:
For the expression tan(89.999°) = 1 / tan(0.001°) my new (2012) HP 35s still gives the inaccurate value (57295.7795401) that users were complaining about way back in 2007. The correct value is:
57295.7795072645567033655767369...
My first diagnosis was that it could have been due to the followingbeginner's mistake in the implementation of the tangent function:
The typical way to compute the tangent function quickly and with high precision isto use an optimal polynomial approximation for values of x whosemagnitude doesn't exceed 45° = /4 (beyond that, you compute the reciprocal of tan(90°-|x|) instead).
If you were to use directly a standard Chebychev economization of tan(x) for the aformentioned polynomial approximation, you'd be essentiallyminimizing the absolute error on a function that may vanish (at x=0). The fairly large relative errors in the neighborhoodof x=0 would result in floating-point values that would be erroneous at their nominal precision.
Instead, you obtain an acceptable polynomial approximationby multiplying x into a Chebychev economization of tan(x)/x (which is itself a poplynomial in x2 ).
Well, whatever mistake the HP engineers did does not reduce to the above. They seem to have implemented correctly the sine function (for which the above warning would have applied too) and the cosine function. Yet, the ratio sin(x)/cos(x) gives exactly the above erroneous value for x = 89.999°. This is a clue that they "cut corners" by wronglyimplementing the tangent as a sin/cos ratio, which is not numerically stable...
(2012-11-27) Discontinuitycliffs appear in the complex extensions of some functions.
(2012-12-09) Turing-complete (only marginally less versatile than the HP 33s).
Like other calculator of its class, the HP-35s is programmed by recording thesequences of keys that would be necessary to produce a result. Such sequences may depend on the data-entry mode that's being used (RPN or "algebraic" infix). Therefore a program written with RPN mode in mind willmost probably not execute properly if the calculator is in algebraic mode (and vice-versa).
My recommendation (and the recommendation of everybody whois familiar with the HP-35s) is to always run this calculator in RPN mode and to writeprograms exclusively for that mode (the capability to use an infix entrymode is no more than a misguided marketing decision which can be safely ignored).
User-defined programs are essentially executed like predefined programs, using the"R/S" key ("run/stop") at the top-left corner of the keypad. The blue-shifted function of this key ("PRGM") is to enter theprogramming mode, where you see every recorded instruction appear wih a 4-digitline number.
If all you ever wanted to do was run a single program, what ypu would do isenter the corresponding instructions staring with line 0001 and execute thesequence by making the program counter point to the beginning (by pushing GTO 1) before hitting the R/S key. It's optional to start such a lone program with a "label" and to end it with the RTN instructionbut we may as well get into the habit of doing it (since it's mandatory if westored more than one program, as will be discussed later). The single-letter "label" (here A) is the name of the routine and will appearas the first character in the line numbers for that routine (which canhave at most 999 lines in it).
Example: To compute the area of a circle of given radius:
