Building, measuring and numbers
The measurement of distance or length may require a numbering system to be able to represent increments of values less than 1 (fractions). History has shone several ways of expressing fractions. Some are listed below:
Sumerian - Fractional values were integrated in their base 60 place value system. The place values did not have a decimal point to mark where the fractional place values started, rather the place values were implied from the context of their usage. base60 (Sexagesimal)
Egyptian - Fractions were used and the numerator was always 1. 3/4 would be notated as 1/2 + 1/4. For more information about the Egyptian numbering system, see the following site. http://eyelid.ukonline.co.uk/ancient/numbers.htm.
Roman - A fraction's denominator was always a factor of 12. These were the Duodecimal fractions. base12 (Duodecimal)
Ratios, geometric relationships and mathematical formulas may facilitate certain types of building and construction. The following are some aspects of a numbering system that would help in this respect:
The use of special symbols to represent numbers rather than using letters of the alphabet or pictures of tally sticks or hands, people, etc.
The use of a place value system so numbers may be expressed somewhat consistently. The use of a place value also vacillitates the ability to calculate numbers with computer like methods, for example the abacus. See the following site for information about the Abacus
The use of a symbol for 0 to denote that a certain place value need not be considered in determining the value of a number. For example 101 in our decimal system means 1 group of 1, no groups of ten and 1 group of 100.
The Indian culture provided a numbering system with the above properties. The Hindu texts included many mathematical considerations. For example, over a thousand years ago a Hindu family may be instructed to build a square shaped alter that occupied the same area as a circular shaped alter. It is not suprising that the Indian culture had the soonest and closest approximation to PI. The Indian culture is credited wih bringing trigonometry to an expressable stage.
The Arabian culture was able to express numbers as a relationship between other numbers and to manipulate the equation expressing that relationship. The word, Algebra is derived from the Arabian term al-jabr which stood for the ability to move a value from one side of an equation to the other side while changing its sign and thus keeping the integrity of the equation intact.
The developement of the Pythagorean Theorum which greatly enhances the ability to build with square corners (by being able to calculate the measurement of the diagonal) is credited to several cultures, the most mentioned and documented is the early Greek culture of which Pythagoras was a member. He is said to have done much travelling to Egypt, Arabia and India and thus could have received insites to its formation from these cultures. The Indian culture has documented evidence of knowlege of the relationships of the sides of a right triangle and the Egyptian culture alludes to the relationships.
The Pythagoreans saw great significance about the relationships of number and attributed many levels of meaning to numbers and their relationships. Symbolism and Number.
See Some ActiveX controls involving algebra and trigonometry
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Last update on 01/26/98
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