Roman Mathematics

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Roman Mathematics
Introduction
 
The system of Roman numerals that we know today is a numeral system that originated from ancient Rome, and was adapted from Etruscan numerals. The system used in antiquity was slightly modified in the Middle Ages to produce the system being used today. The grandeur days of Rome did not emphasize on mathematics as a discipline and discover new abstractions. The Romans were more absorbed in applying mathematics in engineering and architecture to improve the quality of their lives.  

This chapter presents the developments in the history of Roman mathematics and the engineering feats of the Romans.

5.1 The Roman Numerals in Ancient Rome
The Roman numerals of old were derived from the Etruscans. The Roman numerals that are now written with letters of the Roman alphabet were originally separate symbols. THE ROMAN NUMERALS
I – it is descend from a notch scored across the stick or the tally sticks. V – As well it is from the tally sticks but every fifth notch was double cut. X – It is the cross cut form of the tally stick.

L – was written variously as N, И, K, Ψ, ⋔, etc., this had flattened to an inverted T by the time of Augustus. C - was written as Ж, ⋉, ⋈, H, or as any of the symbols for 50 above plus an extra stroke then it is written as >I< or ƆIC, was then shortened to Ɔ or C, with C finally winning out because, as a letter, it stood for centum. D - 500 were like a Ɔ becoming a struck-through D or a Ð by the time of Augustus, under the graphic influence of the letter D. M - 1000 was a circled X: Ⓧ, ⊗, Some variants, such as Ψ and CD, were historical dead ends, while two variants of ↀ survive to this day. One, CIƆ, lead to the convention of using parentheses to indicate multiplication by 1000. ZERO - In general, the number zero did not have its own Roman numeral. Is it IIII or IV?

Originally, it was common to use IIII to represent "four", because IV represented the God Jove. Calendars and clocks
Clock faces that are labeled using Roman numerals conventionally show IIII for 4 o'clock and IX for 9 o'clock, using the subtractive principle in one case and not in the other. There are several suggested explanations for this: The four-character form IIII creates a visual symmetry with the VIII on the other side, which IV would not. IIII was the preferred way for the ancient Romans to write 4, since they to a large extent avoided subtraction. It has been suggested that since IV is the first two letters of IVPITER, the main god of the Romans, it was not appropriate to use. The number of symbols on the clock totals twenty Is, four Vs, and four Xs; so clock makers need only a single mold with five I's, a V, and an X in order to make the correct number of numerals for the clocks. The alternative uses seventeen Is, five Vs, and four Xs, possibly requiring several different molds. The I symbol would be the only symbol in the first 4 hours of the clock, the V symbol would only appear in the next 4 hours, and the X symbol only in the last 4 hours. This would add to the clock's radial symmetry. IV is difficult to read upside down and on an angle, particularly at that location on the clock. Louis XIV, king of France, preferred IIII over IV, ordered his clockmakers to produce clocks with IIII and not IV, and thus it has remained. Clocks originally did not have hands, they only chimed the hour. There was a different chime tone for me, V and X. By having four IIII's, the wooden cog wheel could be made without an additional clog and be more economical. Roman clockRoman calendar

Is it XCIX or IC?
Rules regarding Roman numerals often state that a symbol representing 10x may not precede any symbol larger than 10x+1. For example, C cannot be preceded by I or V, only by X (or, of course, by a symbol representing a value larger than C). Thus, one should represent the number "ninety-nine" as XCIX, not as the "shortcut" IC. However, these rules are not universally...
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