Virnaculum

Virnaculum is a Latin word that means chain or tie. It is a mathematical operation that means or indicates that terms under or above it are together and should be given priority while solving any BODMAS problem. BODMAS as we all are aware means Brackets, order Division Multiplication Addition and subtraction but when we see this bar like symbol known as Virnaculum than we have to follow the mnemonic VBODMAS that means Virnaculum , Bracket ,Order, Division Multiplication,Addition and subtraction.

Virnaculum is given priority if it is present while solving any mathematical problem. 

Coming on to the usage Earlier vinculum was used widely to indicate that the given terms are together but now this function is replaced by parentheses or the round brackets or in some cases it is also used to indicate recurring decimal .For example in the case of 0.99999999 we can write it as 0.9 and a bar above 9

History 

Vinculum was introduced by Frans van Schooten in the year 1646.Also some early attempts were made by scientists like Chuquet in the year 1484 and Descartes in the year 1637.

Uses or Application 

In modern days the uses of vinculum has been in three main ways these are as follows -:

• As a Boolean logic – it is used in Boolean operators to symbolise NOT or inversion of operation.For example- Y= AB 
• Used in geometry – In geometry the symbol of bar or vinculum  is used to indicate a line segment . For example -AB wherein A and B are the two end points of the line segment.
• Use in recurring decimal-The bar or vinculum is used to indicate a recurring or repeating decimal.For Example in the case of ⅓ = 0.3333333

Historical uses 

• As a Grouping device – It serves the same function as the parentheses. To indicate a group in a given equation.For example a×b-c the bar on b minus c indicates that b minus c is together and that first the subtraction of the to will take place followed by the multiplication with a.

• Part of radical-: it is used with the radical sign √ with the vinculum to give the under root symbol which is widely used today .This symbol was given by Descartes in the year 1637

Rules of simplification with Virnaculum 

1. Look at the equation carefully and the operations that are present.
2. If the given question has a virnaculum then solve that part first irrespective of Any thing as the rule says VBODMAS. Hence virnaculum precedes any other Operation.
3. Further look for Brackets according to the rule. If Brackets are present then remember to solve the Brackets in the correct order. As we know there are three main types of Brackets that are widely used in mathematics; these are the round brackets , curly brackets and the box or round brackets . Talking about the priority or hierarchy of solving or opening these Brackets is as follows – Round brackets followed by curly Brackets and the last the box Brackets or the box Brackets are to be solved .So simply put (){}[] round – curly – box Brackets.
4. Order of an equation is the power or exponent of the given equation.If the equation has any exponent in the equation then after Brackets that has to be tackled and treated.
5. After Orderlook for division or multiplication from left to right order.
6. Followed by addition or subtraction in the left to right Order.

Algorithm 

How to solve virnaculum 

The below algorithm shows the correct order to be followed in problems related to Virnaculum simplification .

Step 1: Observe the equation 

Step 2 : Virnaculum present, solve and simplify that part and move to Brackets.

Step 3 : Look for Brackets . Identify the Brackets and remember the order or hierarchy of solving.First solve the round brackets followed by the curly brackets and finally the box or square brackets.

That is ()-{}-[]

Step 4: Order of the equation is solved if present . It is the Power of the equation under consideration.

Step 5: Division followed by multiplication from left to right .

Step 6: Addition and Subtraction followed from left to right side.

Example (bold text has bar over it )

•  12-[ 3960÷{ 8+2(43- √121+6×7)}]

Answer 

12-[ 3960÷{ 8-2(43+√121+6×7)}] first solve the Virnaculum part 6×7 that is 42 and the Brackets order wise.

12-[ 3960÷{ 8+2(43- √121+42)}]

12-[ 3960÷{ 8+2(64-11+42)}]

12-[ 3960÷{ 8+2(64-11+42)}]

12-[ 3960÷{ 8+2(95)}]

12-[ 3960÷{ 8+190}]

12-[ 3960÷198]

12-20

-8 is the answer

Conclusion 

Virnaculum is a Latin word that means tie or chain. The Symbol for Virnaculum is a horizon line or bar. It is used for a variety of purposes. As per history the Virnaculum was used as a parentheses of earlier days . Basically the Virnaculum means considering the objects under its influence as together and hence they are solved together. Modern day application of Virnaculumn is that it is used as a Boolean operators in physics , it is also used as a symbol to indicate line segment in geometry with the alphabets above which it is drawn as the end point of that segment and also as a indication of recurring or repeating digits. It is a symbol used to signify repeating digits or terms in a decimal .Thus virnaculum is of great usage in simplification problems .