Invasion of Greek civilization by Romans gave rise to Roman Empire. Roman Empire started invasion over Greeks around in 300 BC and gaining complete invasion over them around in 100 AD. But Romans were not as good as Greek in geometry so they did not had much contributions in geometry. Also Romans used mathematics just for practical purposes like trade, division of land, creating buildings, etc and also due to the cumbersome nature of Roman numerals they could not go much beyond the simple arithmetics which was also not easy to learn. Roman Numerals are used even today especially were large numbers are not required like on clocks, writing page numbers in the book before the index page, etc. Initially like 1-3; 4 was written as IIII and 9 was written as VIII. But later 4 was written as IV which means (V-I) and similarly 9 was written as IX (X-I) and I in such numbers is called as subtractive prefix. It comes very handy when we have very big and repetitive numbers. Example 1947: 1000 + 900 + 40 + 7 = 1000 + 500 + 4(100) + 4(10) + 7 = MDCCCCXXXXVII = MDCDXLVII (CCCC= 400 = 500-100 = CD. Similarly XXXX=XL) = MCMXCVII (DCD = 500+400= 900= M-C = CM) Roman Addition Rules: Convert subtractive prefixes to normal (Eg: IV = IIII; IX = VIIII). Concatenate both the numbers (in descending order). Do normal sums like (IIIII = V but don’t write IIII=IV; VV = X) Final answer should be in subtractive prefixes if required. (Final answer should not have VIIII, convert to IX) Example: 106 + 94 = CVI + XCIV = CVI + LXXXXIIII (Rule 1) = CLXXXXVIIIII (Rule 2) = CLXXXXVV (Rule 3) = CLXXXXX (Rule 3) = CLL (Rule 3) = CC (Rule 3) =200 Roman Subtraction Rules: Convert subtractive prefixes to normal (Eg: IV = IIII; IX = VIIII). Remove common symbols (VIII- IIII = VI - I). No number should be present after – sign, else keep writing number present before – sign normally (CXXX – VII; Expand one X and remove common symbols, if still number … [Read more...]
Greeks
Greek Mathematics Although Greek civilization began from 2000 BC, it is believed that Greek Mathematics started around BC 700 which can be divided to periods, Classical Age from 700 – 300 BC and Hellenistic period from 300 BC- 400 AD and location extended from parts of Italy, Libya, Egypt, Greece and Turkey . Initially communication was done orally but later they started making clay tablets similar to Babylonians, writing on Paprus rolls and writing on wooden boards. Greek Numerals Earlier numeral system used was Acrophonic. Later around 4th century BC, it got replaced by Ionic number system where symbols were used instead of numbers. They also used with another system which were similar to Roman numerals and were similar in terms of complicacy as well. Because of their complex number system, like Romans, they were not so go good in arithmetic’s as compared to their expertise in Geometry (We will see more on numerals in Romans topic). Greeks were very good in Geometry. Many great mathematicians like Thales, Pythagoras, Euclid, Archimedes, etc were born in this period. [wptabs style="wpui-narrow" effect="slide" mode="horizontal"] [wptabtitle] Thales[/wptabtitle] [wptabcontent] Thales of Miletus (Today's Turkey) was born around 625/624 BC and died in 547/546 BC. Thales was the 1st Philosopher and mathematician of Greek civilization and he is believed for starting western philosophy. None of his work survived today but in those days they used to transfer the knowledge orally and was passed to the pupils which in turned passed to the next generation. It is believed Pythagoras was pupil of Thales. In his teenage life he visited Egypt, stayed and learnt there and then brought geometry to Greece. During his stay in Egypt he successfully was able to measure the height of pyramids using the geometrical properties of similar triangles and the length of shadows. He would wait till his height and his own shadow’s height match each other and then he would … [Read more...]