Javascript RPN Scientific Calculator
Reverse Polish Notation (RPN) is a mathematical notation that has been in use for several decades. It is a postfix notation in which operators are placed after their operands. This notation is also known as postfix notation because the operator comes after the operand. In this article, we will explore Reverse Polish Notation and how it can be used in mathematical calculations.
Introduction
Reverse Polish Notation (RPN) is named after its Polish creator, Jan Łukasiewicz. The notation was introduced in 1920 and gained popularity in the 1960s and 1970s. RPN is used in calculators, programming languages, and computer systems.
RPN Calculation
RPN has many advantages over other notations, such as infix notation. One of the primary advantages of RPN is that it eliminates the need for parentheses in mathematical expressions. RPN has a fixed order of operations, which makes it easier to write programs and perform calculations.
The RPN calculator works by accepting input in postfix notation. It reads each operand and operator and performs the necessary calculations. For example, if we have the expression "5 3 +", the RPN calculator will read the operands 5 and 3, and then the operator "+". It will then perform the addition operation and return the result, which is 8.
RPN Syntax
RPN has a simple syntax. It consists of operands and operators separated by spaces. The operator comes after the operands. RPN does not use parentheses or brackets to specify the order of operations.
RPN Operators
RPN supports many operators, including addition, subtraction, multiplication, division, and exponentiation. It also supports trigonometric and logarithmic functions. The following table shows some of the most commonly used operators in RPN.
| Operator | Description | Example |
|---|---|---|
| + | Addition | 2 3 + |
| - | Subtraction | 5 2 - |
| * | Multiplication | 4 3 * |
| / | Division | 6 2 / |
| ^ | Exponentiation | 2 3 ^ |
| sin | Sine | 90 sin |
| cos | Cosine | 60 cos |
| tan | Tangent | 45 tan |
RPN Example
Let's take a simple mathematical expression as an example, "2 + 3 * 4 - 5". In infix notation, we would have to use parentheses to specify the order of operations. However, in RPN, we can write this expression as "2 3 4 * + 5 -". This expression can be evaluated by a calculator that supports RPN.
In this example, the RPN calculator will first read the operands "2", "3", and "4". It will then read the operator "*". It will perform the multiplication operation and push the result "12" onto the stack. It will then read the operand "2" and push it onto the stack. It will read the operator "+" and perform the addition operation, pushing the result "14" onto the stack. It will then read the operand "5" and the operator "-", performing the subtraction operation and pushing the final result "9" onto the stack.
Conclusion
Reverse Polish Notation is a powerful mathematical notation that eliminates the need for parentheses and brackets in mathematical expressions. It has many advantages over other notations, such as infix notation. RPN is widely used in calculators, programming languages, and computer systems. Understanding RPN and its syntax can help in performing complex mathematical calculations with ease.
