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Vinculum or virnaculum was used to describe that some terms are together or in a group.It is a Latin word that means tie and hence tied together is the meaning of the symbol . 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.Now the function if virnaculum is to indicate repetition of something.for example in the equation given below the number 5 is repeating or recurring decimal
6-(7÷4+2.555555) or we can say 6-(7÷4+2.5)( bold letter has a bar on the top )
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.
Simplification of Virnaculumn
Example No.1 ( bolded portion is under bar)
9/10-[⅕+{¼+(⅚+⅓+½)}]
Answer No.1
In the above mentioned problem the part under virnaculum that is ½ and ⅓ will be first solved followed by round brackets than curly brackets than box brackets and finally the part outside to get the final answer.
So first we will add ⅓ and ½ , taking LCM of 2 and 3 we get 6 so 2+3/6 that is ⅚.
We will add this to ⅚ and the equation goes like –
9/10-[⅕+{¼+(⅚+⅚)}]
9/10-[⅕+{¼+10/6}]
9/10-[⅕+{3/12+2/12}]
9/10-[⅕+5/12]
9/10-[37/60]
45/60-37/60
8/60
2/15 is the answer to the problem
Example No. 2
18-[8÷2{8÷4×1}]
Answer No.2
In the above mentioned question the terms under virnaculum are 4×1 that is 4 followed by curly and box bracket.
The solution is as follows -:
18-[8÷2{8÷4}]
18-[8÷2{2}]
18-[8÷4]
18-2
16 is the answer to the given question.
Example no.3
a-[a-{a+(a-a+b)}]
Answer no.3
a-[a-{a+(a-a+b)}] in this a+ b is under virnaculum hence that will be solved followed by brackets (){}[]
So the solution is as below-:
a-[a-{a+(a-a+b)}] a+ b is done
a-[a-{a+(-b)}] as a-a = 0
a-[a-{a-b}] sign change on opening brackets
a-[a-a+b] a and -a got cancelled
a-[b]
a-b us the answer of the given problem
Conclusion
Virnaculum or Vinculum is the horizontal line or bar used in mathematics. It is a mathematical operation that is derived from a Latin word vinculum meaning chain or tie. Similar to its function the bar or the horizontal line symbolises that the terms below or above it are grouped together. In early days it was used as a parentheses or as a part of radical to form the modern day under root symbol.The earliest attempt to introduce vinculum was done by Chuquet.
Virnaculum finds its application in modern day mathematics to indicate a line segment ,used in Boolean operators to indicate the inversion or NOT of any operation and in a recurring decimal where the repeating term is written with a bar on top.
