Search results
Results From The WOW.Com Content Network
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]
Sin continued to be worshiped in Sippar under Persian rule as well. [260] In Larsa Sin was worshiped in a temple shared with Ningal in the Old Babylonian period, but no references to him occur in sources from this city from later times. [261] Sin and Ningal at some point replaced Inanna and Dumuzi as the tutelary deities of Kissig. [262]
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
The apparent size of the Sun and the Moon in the sky. The size of the Earth's shadow in relation to the Moon during a lunar eclipse; The angle between the Sun and Moon during a half moon is 90°. The rest of the article details a reconstruction of Aristarchus' method and results. [4] The reconstruction uses the following variables:
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 ...
Let PQ be a line perpendicular to line OQ defined by angle , drawn from point Q on this line to point P. OQP is a right angle. Let QA be a perpendicular from point A on the x -axis to Q and PB be a perpendicular from point B on the x -axis to P. ∴ {\displaystyle \therefore } OAQ and OBP are right angles.
Some Greek measures of length were named after parts of the body, such as the δάκτυλος (daktylos, plural: δάκτυλοι daktyloi) or finger (having the size of a thumb), and the πούς (pous, plural: πόδες podes) or foot (having the size of a shoe).
An optical imaging system (gray box) that obeys the sine condition has a fixed ratio between the sines of the ray angles at the entrance and exit of the system, sin(α o) / sin(α i), that equals the magnification M. Using the framework of Fourier optics, we may easily explain the significance of the Abbe sine condition.