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Sometimes a piece is written with multiple time signatures simultaneously. For example, it might specify 4/4 2/4 3/4 5/4, meaning that the length of measures is irregular and can be 4, 2, 3 or 5 quarter-notes. The time signature of the first measure is always specified first, and the others are placed in increasing order of length.
"Look toward heaven and count the stars, if you are able to count them." And He added, "So shall your offspring be."(Genesis 15:5.). Bemidbar, BeMidbar, B'midbar, Bamidbar, or Bamidbor (בְּמִדְבַּר —Hebrew for "in the wilderness of" [Sinai], the fifth overall and first distinctive word in the parashah), is the 34th weekly Torah portion (פָּרָשָׁה , parashah) in the ...
The space groups with given point group are numbered by 1, 2, 3, ... (in the same order as their international number) and this number is added as a superscript to the Schönflies symbol for the corresponding point group. For example, groups numbers 3 to 5 whose point group is C 2 have Schönflies symbols C 1 2, C 2 2, C 3 2.
The tetractys. The tetractys (Greek: τετρακτύς), or tetrad, [1] or the tetractys of the decad [2] is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number.
Bhāskara (c. 600 – c. 680) (commonly called Bhāskara I to avoid confusion with the 12th-century mathematician Bhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to write numbers in the Hindu–Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's ...
For example, the digits shown here for 3 and 4 were in some manuscripts swapped with those for 7 and 8, and the 5's may be written with a lower dot (꜎ etc.), with a short vertical stroke in place of the dot, or even with a triangle joining to the stave, which in other manuscripts indicated a 9.) [13] [1]
Hence all centered square numbers and their divisors end with digit 1 or 5 in base 6, 8, and 12. Every centered square number except 1 is the hypotenuse of a Pythagorean triple (3-4-5, 5-12-13, 7-24-25, ...). This is exactly the sequence of Pythagorean triples where the two longest sides differ by 1. (Example: 5 2 + 12 2 = 13 2.) This is not to ...
N(4, 4) = 1 path with 4 peaks: The sum of N ( 4 , k ) {\displaystyle \operatorname {N} (4,k)} is 1 + 6 + 6 + 1 = 14, which is the 4th Catalan number, C 4 {\displaystyle C_{4}} . This sum coincides with the interpretation of Catalan numbers as the number of monotonic paths along the edges of an n × n {\displaystyle n\times n} grid that do ...