Registers – Calculators – Input-output calculator to indicator – printer – etc.
Reexamination Certificate
2003-02-03
2004-11-23
Frech, Karl D. (Department: 2876)
Registers
Calculators
Input-output calculator to indicator, printer, etc.
C708S131000
Reexamination Certificate
active
06820800
ABSTRACT:
The present invention relates to electronic calculators and in particular to calculators of the kind commonly used at present by most people and especially by schoolchildren and students,
The widespread use of calculators by schoolchildren and students has over the years tended to engender complete reliance on them at the expense of the student's losing quantitative conception, feel for numbers and the ability to carry out calculations by mental arithmetic, even approximately.
One attempted solution to this problem has been simply to attempt to ban the use of calculators in certain situations. This too is wrong. Once people having mastered manual arithmetic for them to continue to do so manually only is a waste of time. The use of calculators is there to avoid this waste of time. Also, manual calculations, such as long multiplication and long division, often do not throw much light on the expected values and are prone to undetected gross mistakes.
The present invention is concerned with providing a calculator which addresses these problems and provides a solution which reconciles the currently contradictory demands and views associated with this problem. The present invention is concerned with getting schoolchildren and students who use calculators to actually do some thinking as they do so.
According to the present invention, there is provided an electronic calculator having means for enabling a user to input a calculation, characterised in that the calculator has a mode of operation in which, after entering a calculation to be performed by the calculator, the user is required to input additionally an estimate of the result of the calculation and, for at least a predetermined number of attempts, the result of the calculation is displayed by the calculator only if the estimate lies within a predetermined tolerance range of the correct result.
In the preferred embodiment of the invention, the tolerance range is determined by the calculator in dependence upon the nature of the operators, the numerical value of the operands in the calculation and any tolerance range of the operands.
There now follows an explanation of the intended meaning of a number of terms which are used in this patent specification:
Predetermined Tolerance
This term could refer to a fixed tolerance expressed either as an absolute value (for example ±10) or as a percentage of the result (for example ±10%). In the preferred embodiments described below, however, this term is used to refer to a case-specific actual tolerance which is worked out by the calculator using predetermined rules or algorithms, that is, rules that are built into the calculator for establishing the actual tolerance for each particular case of operation type and operands value and their previously established tolerances, if any.
Operations String
The term refers to an arithmetic calculation which comprises at least two distinct stages or arithmetic operations. For example the sum A+B comprises a single stage and single operator ‘+’ whereas the sum (A+B)·C comprises two stages and two operators, namely addition operator ‘+’ and multiplication operator ‘·’. Thus an operations string includes at least two operators and/or functions e.g. sin (A+B), the operators being ‘sin’ and ‘+’.
Type of Calculator
The present invention is applicable to the range from so-called four function calculators to typical so-called scientific calculators (i.e. containing some or all of trigonometric, exponential, logarithmic, roots, reciprocal, factorial function keys) which employ numbered memories, multi-level brackets, M+ and M− keys and correct operations order hierarchy, i.e.: function, ‘·’, ‘÷’, ‘+’ and ‘−’, e.g. if the keyed in order is A+B·C cosine, cosine C is evaluated out first, then this result is multiplied by B and to this result A is added.
Operations Strings and Tolerances
Unless stated otherwise the display displays only keyed in numbers and no intermediate result. There are two approaches to calculating the tolerances which apply to an operations string i.e. to calculations which have at least two stages or operators.
Approach I is to have the tolerances of the operations built up successively as the calculation progresses through the string of stages from beginning to end, i.e. the total end tolerance is some form of accumulation of the individual tolerances of the successive stages. Only upon ‘=’ has the user to key in the estimate which is then checked by the calculator, and if it is found to be within the total end tolerance the correct result is displayed. Thereafter, if the user wishes, he can continue with further stages, using the result of the previous ‘=’ as the next operand.
Approach II would be to halt the calculation after every stage, test the user's estimate against the correct answer up to that point and if within the acceptable tolerance then display the correct result of the sub-calculation and then continue with the next stage using the correct intermediate figure as its starting point.
Tolerances
Each stage in a string (or where there is only a single stage) consists of operand 1, operator, operand 2, or example
4·5,
or operand, function, operand 2 if required by function, for example
31 sine (or sin(
31
)−in EOS), or 3 x
y
6.2 (these are the keys that have to be operated.)
The operands are either keyed in numbers, or memory recall numbers or, in cases of strings, results from previous stages. The operation of each stage of the calculation receives a ‘±’ tolerance which is the acceptable range for the mental estimate of this operation.
In the simplest case, that of a single stage (or always in Approach II) e.g. A+B or A·B (A and B being keyed in numbers), the tolerance is calculated according to the rules relating to the respective operation, hereafter referred to ‘tol(op)’. The rules are detailed later.
In Approach I, in the case of a stage in the string where both operands are results of previous stages, e.g.: the adding stage in A·B+C/D, it is necessary to represent the fact that the added quantities already have a tolerance which resulted from the earlier stage in which they were calculated, namely, the tolerances resulting from the multiplication A×B and division C/D. Therefore the total tolerance after the addition stage in A·B+C/D is the combination of tol(A·B), tol(C/D) and the tolerance of the addition. Using E for the result of A·B and F for the result C/D the tolerance following the addition can be written as
tol(E) “+” tol(F) “+” tol(op); tol(op) in this case is tol(+).
The addition operator is placed in inverted commas to express the fact that tolerances are not necessarily added up arithmetically but could be cumulatively combined in other ways e.g. RSS (Root Sum(of) Squares) specifically for +, − operations the combined absolute tolerances would be the RSS of the absolute values of the tolerances of the operands and the tolerance of the operation (see example [E.
4
] below), while for ·, ÷ operations the combined relative tolerance would be the RSS of the relative value of the tolerances of the operands and the operation.
Considering the tolerance of the adding stage of A·B+C where the A·B has already been carried out and C is keyed in the complete tolerance is built up from the tolerances resulting from the A·B stage and from tol(+). (C has no tolerance because it has been keyed in).
Thus, in Approach I in a lengthy string e.g. A+B·C−D/E+F·G·H=the tolerance would build up until the ‘=’ is keyed in.
However there are certain cases where the user will preferably have to be asked to make intermediate estimates. This is associated with the prevention of means of extracting the correct result from the calculator without doing any mental arithmetic. The following are circumstances in which such intermediate estimates will be preferably required:
i) When the user closes a bracket. For example in the sum
Fleit, Kain, Gibbons, Gutman, Bongini & Blanco P.L.
Frech Karl D.
Gibbons Jon A.
Messulam Alec
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