Can someone give me some information on the Base 5 number system?

Question

For example its history, who used it, who invented it, how it was invented, ect. I know what it is, but I would like to know its backround.

Answer 1

Base-5 is one of the most primative counting systems. It was used primarily before the writing of numbers. The signs or words used are hand for 5, two hands for 10, person for 20 (two hands and two feet).

Some cultures would count on fingers with 0 being a closed fist and putting a finger up for one, etc, and some cultures would have 0 being an open hand and 1 would be signified by putting a digit down with 5 represented by a closed fist or 5 down.

Base 5 was used not as a formalized place value, but rather as a grouping value that combined with other values to a larger grouping value. For example 2 fives (two hands) are 10, 4 fives (two hands and two feet-or person) are 20. 12 fives are 60. Each of the groups 10, 20 and 60 were developed into more rigorous numbering systems throughout our globe's cultural history.

The use of 5 as a grouping value is easily understood as the hand has 5 digits. This grouping was used for several hundreds of thousands of years by many cultures around our globe.

In the twentieth century, only the East African Luo tribe of Kenya and the Yoruba of Nigeria were still using a base-five system. However, the base-ten (denary or decimal) system has prevailed in most areas and these tribes, like most previously quinary-counting cultures, have converted.

Base-5 is still in use in a few places. For example merchants near Mumbai, India will use a base-5 counting system for figuring totals. This allows them to perform calculations on one hand while serving their customers with the other.

Many ancient cultures (Roman, Chinese, Japanese) also used an abacus for counting. While an abacus is generally used for base-10 calculations, they have a foundation in both base-5 and base-2. They often have a dividing bar with 5 beads below and 2 beads above for the base-5 and base-2 part of a number.

Answer 2

All number systems that use a Base require the number 0. An example of a system that does not use the Base system and also does not make use of zero is the Roman Number System. With the Roman Number system it is not possible to have an algorithm to add, subtract , multiply or divide two numbers. The zero used in the decimal system and the base 5 system makes it possible to do the above operations. Therefore I would say that the person who invented the number zero is also responsible for all the number systems that have a base, including base 5. In our history books a mathematician called Aryabhatta who lived about 2600 years ago in India invented the number zero and can therefore be considered the inventor of all the Base systems (Base 10, Base 5, Base 2, or Base 8, Base 16 etc) The Indians needed the system to do trignometric calculations to study the movements of the stars.

Answer 3

The now-extinct Saraveca language of South America used base 5.

Oh, and it is most assuredly possible to "have an algorithm to add, subtract , multiply or divide two numbers" using the Roman numbering system. In fact, it's simpler (though slower) than our own system for adding: just combine and regroup as needed. Multiplication was usually done with abacuses or with Egyptian-style doubling tables. Division was done with table lookup and refinement (and was especially slow). Subtraction is like addition, except you break up symbols as needed instead of carrying.