In this blog I will be emphasizing:
interesting topics
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Language deals with letters as math deals with numbers. Without numbers there would be no math. So let's get started by recognizing the history of numbers and how they came around....
Numeration Systems
On Thursday January 27th, we learned that there were several other ways to write numbers other than the way we do today. Most of the ways are extensive and can be confusing at times, which is why we no longer use them.
Numerals: written symbols for numbers
Numeration System: a locally organized collection of numerals
The earliest numeration system appears to have grown from tallying.
© Annenberg Foundation 2011
Each tally stroke represents one. When there are a total of five tallies per set, a diagonal is used. Tallies are very easy to use. I remember using them all throughout elementary school and even in high school when we would play games and keep score.
Base: the number of objects used in the grouping process
Base-ten numeration system: when grouping is done by 10s
Ancient Numeration Systems
- Egyptian Numeration
Made by Fleur de Roos, Ilse De Waele, Vanessa Heyndrickx
September 1998
September 1998
Shown above a stick represents numbers 1-9. A heel bone represents 10, a coiled rope represents 100, and a lotus flower represents 1,000. The symbols continue with a pointing finger representing 10,000, a frog (sometimes written as tadpole) representing 100,000 and finally a Pharaoh's kneeling slave representing 1,000,000.
This number system is an example of an additive numeration system, because each power of the base is repeated as many times as needed.
Can you imagine drawing all of these pictures for every single number you used?! I can't imagine how many pieces of paper one algebraic expression would use.
- Roman Numeration
© 2000-2011 Nicholas Academy
The Romans wrote their numerals so that the numbers they stood for were in decreasing order from left to right (Bennett, Burton, Nelson). When a Roman Numeral is placed in front of a numeral for a larger number its position indicates subtraction. This is shown, for example, in the Roman Numeral for the number 9. It would be written as IX. Showing that one is subtracted from ten.
Roman Numerals are over all simple to understand, however, I think it is one of the numeration systems that has been forgotten. Kids today may not even know what they mean. This chart is very helpful in showing what each numeral stands for. Also unlike the other systems the Roman Numerals do not take long to write.
- Babylonian Numeration
©2005-2011 Red Gate Software
The example shown above is a number much larger than 59. To write numbers larger than 59 the Babylonians used their basic symbols for 1-59 and the concept of place value.
Place Value: a power of the base
The Babylonian place values were 1, 60, 60² , 60³ , etc. The symbols have different values depending on the position or location of the symbol. Above the (1*60²) makes 3600 and the (2*60) makes 120. Add the two together the total is 3720. Add this to the 36 and the number 3756 is the outcome. This system was very particular, therefore, the smallest mistake could change the number entirely.
The Babylonian System seems very confusing to me. I can easily see why it is no longer used. Writing out the number 100 would take some time and thinking. The fact that the placement of each symbol matters can be very confusing as well. The example problem shown above helped me understand the concepts of Babylonian numbers. It also showed the shorthand way of writing numbers and problems.
- Mayan Numeration
J J O'Connor and E F Robertson
As shown numbers greater than 19, place values were used. The Mayans wrote their numerals vertically with one numeral above another. The powers of the base increase from the bottom to the top. The numeral in the bottom represents the number of units. The numeral in the second position represents the number of 20s.
The Mayan Numeration System is very clear and easy to comprehend in the chart above. It makes sense and was one of the best systems during its time. The Mayans were the only group to include the number zero. That says something right there.
- Hindu-Arabic Numeration
In English the number names for whole numbers from 1-20 are all single words. The names for numbers 21-99 are compound number names that are hyphenated. Except for the numbers 30, 40, 50, etc...
Obviously this is the shortest system of them all. It has been very successful for many years and that is why it is the one we use today.
© Puentes
Aren't you glad we don't use Hieroglyphics, or the Babylonian Number System!? Could you imagine doing algebra and calculus problems with all of those symbols?! Problems are hard enough with our number system today. I think it's interesting how numbers have developed over time, and I am very thankful they have =)
