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To compensate for the lack of a table of chords, mathematicians of Aristarchus' time would sometimes use the statement that, in modern notation, sin α/sin β < α/β < tan α/tan β whenever 0° < β < α < 90°, now known as Aristarchus's inequality. [16]
The Books of Samuel portray the Temple as having a Phoenician architect, and in Phoenicia it was the Babylonian ell which was used to measure the size of parts of ships. [1] Thus scholars are uncertain whether the standard Biblical ell would have been 49.5 or 52.5 cm (19.49 or 20.67 in), but are fairly certain that it was one of these two ...
38,000 BCE: The Aurignacian [9] Löwenmensch figurine, the oldest known zoomorphic (animal-shaped) sculpture in the world and one of the oldest known sculptures in general, was made. The sculpture has also been interpreted as anthropomorphic, giving human characteristics to an animal, although it may have represented a deity.
Since the chart combines secular history with biblical genealogy, it worked back from the time of Christ to peg their start at 4,004 B.C. Above the image of Adam and Eve are the words, "In the beginning God created the Heaven and the Earth" (Genesis 1:1) — beside which the author acknowledges that — "Moses assigns no date to this Creation.
The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
30.823: 184.94: Area. The ordinary units used for land measurement were: ... the Greek day began after sunset. ... and in Hellenistic times years were reckoned in ...
Islamic centuries to corresponding Gregorian years [5]. 1st century AH (622 – 719 CE); 2nd century AH (719 – 816) 3rd century AH (816 – 913) 4th century AH (913 – 1009)
The area of triangle OAD is AB/2, or sin(θ)/2. The area of triangle OCD is CD/2, or tan(θ)/2. Since triangle OAD lies completely inside the sector, which in turn lies completely inside triangle OCD, we have < < .