241
Pharmacy / Re: Avoid Milk Tea
« on: March 06, 2012, 05:00:32 PM »
Madam thanks for the post
News:
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243
Pharmacy / Re: HOW TO STAY YOUNG and enjoy the life
« on: March 06, 2012, 04:57:54 PM »
thanks for the post
244
Pharmacy / Re: 7 easy ways to beat wrinkles
« on: March 06, 2012, 04:57:06 PM »
knowledgeable post
247
BBA Discussion Forum / Re: DIU Permanent Campus
« on: March 05, 2012, 08:03:41 PM »
DIU permanent campus is exquisite.
248
Science Discussion Forum / Area of regular polygon
« on: March 05, 2012, 07:55:18 PM »
The formulae below give the area of a regular polygon. Use the one that matches what you are given to start. They assume you know how many sides the polygon has. Most require a certain knowledge of trigonometry.
area= N*s^2/4*tan(180/N)
where
S is the length of any side
N is the number of sides
TAN is the tangent function calculated in degrees
Note: Unlike a regular polygon, unless you know the coordinates of the vertices, there is no easy formula for the area of an irregular polygon. Each side could be a different length, and each interior angle could be different. It could also be either convex or concave.
One approach is to break the shape up into pieces that you can solve - usually triangles, since there are many ways to calculate the area of triangles. Exactly how you do it depends on what you are given to start. Since this is highly variable there is no easy rule for how to do it.
area= N*s^2/4*tan(180/N)
where
S is the length of any side
N is the number of sides
TAN is the tangent function calculated in degrees
Note: Unlike a regular polygon, unless you know the coordinates of the vertices, there is no easy formula for the area of an irregular polygon. Each side could be a different length, and each interior angle could be different. It could also be either convex or concave.
One approach is to break the shape up into pieces that you can solve - usually triangles, since there are many ways to calculate the area of triangles. Exactly how you do it depends on what you are given to start. Since this is highly variable there is no easy rule for how to do it.
249
Science Discussion Forum / Earliest mathematicians
« on: March 05, 2012, 03:45:29 PM »
Little is known of the earliest mathematics, but the famous Ishango Bone from Early Stone-Age Africa has tally marks suggesting arithmetic. The markings include six prime numbers (5, 7, 11, 13, 17, 19) in order, though this is probably coincidence.
The advanced artifacts of Egypt's Old Kingdom and the Indus-Harrapa civilization imply strong mathematical skill, but the first written evidence of advanced arithmetic dates from Sumeria, where 4500-year old clay tablets show multiplication and division problems; the first abacus may be about this old. By 3600 years ago, Mesopotamian tablets show tables of squares, cubes, reciprocals, and even logarithms, using a primitive place-value system (in base 60, not 10). Babylonians were familiar with the Pythagorean theorem, quadratic equations, even cubic equations (though they didn't have a general solution for these), and eventually even developed methods to estimate terms for compound interest.
Also at least 3600 years ago, the Egyptian scribe Ahmes produced a famous manuscript (now called the Rhind Papyrus), itself a copy of a late Middle Kingdom text. It showed simple algebra methods and included a table giving optimal expressions using Egyptian fractions. (Today, Egyptian fractions lead to challenging number theory problems with no practical applications, but they may have had practical value for the Egyptians. To divide 17 grain bushels among 21 workers, the equation 17/21 = 1/2 + 1/6 + 1/7 has practical value, especially when compared with the "greedy" decomposition 17/21 = 1/2 + 1/4 + 1/17 + 1/1428.)
While Egyptians may have had more advanced geometry, Babylon was much more advanced at arithmetic and algebra. This was probably due, at least in part, to their place-value system. But although their base-60 system survives (e.g. in the division of hours and degrees into minutes and seconds) the Babylonian notation, which used the equivalent of IIIIII XXXXXIIIIIII XXXXIII to denote 417+43/60, was unwieldy compared to the "ten digits of the Hindus."
The Egyptians used the approximation π ≈ (4/3)4 (derived from the idea that a circle of diameter 9 has about the same area as a square of side
. Although the ancient Hindu mathematician Apastambha had achieved a good approximation for √2, and the ancient Babylonians an ever better √2, neither of these ancient cultures achieved a π approximation as good as Egypt's, or better than π ≈ 25/8, until the Alexandrian era.
reference: http://fabpedigree.com/james/mathmen.htm
The advanced artifacts of Egypt's Old Kingdom and the Indus-Harrapa civilization imply strong mathematical skill, but the first written evidence of advanced arithmetic dates from Sumeria, where 4500-year old clay tablets show multiplication and division problems; the first abacus may be about this old. By 3600 years ago, Mesopotamian tablets show tables of squares, cubes, reciprocals, and even logarithms, using a primitive place-value system (in base 60, not 10). Babylonians were familiar with the Pythagorean theorem, quadratic equations, even cubic equations (though they didn't have a general solution for these), and eventually even developed methods to estimate terms for compound interest.
Also at least 3600 years ago, the Egyptian scribe Ahmes produced a famous manuscript (now called the Rhind Papyrus), itself a copy of a late Middle Kingdom text. It showed simple algebra methods and included a table giving optimal expressions using Egyptian fractions. (Today, Egyptian fractions lead to challenging number theory problems with no practical applications, but they may have had practical value for the Egyptians. To divide 17 grain bushels among 21 workers, the equation 17/21 = 1/2 + 1/6 + 1/7 has practical value, especially when compared with the "greedy" decomposition 17/21 = 1/2 + 1/4 + 1/17 + 1/1428.)
While Egyptians may have had more advanced geometry, Babylon was much more advanced at arithmetic and algebra. This was probably due, at least in part, to their place-value system. But although their base-60 system survives (e.g. in the division of hours and degrees into minutes and seconds) the Babylonian notation, which used the equivalent of IIIIII XXXXXIIIIIII XXXXIII to denote 417+43/60, was unwieldy compared to the "ten digits of the Hindus."
The Egyptians used the approximation π ≈ (4/3)4 (derived from the idea that a circle of diameter 9 has about the same area as a square of side
. Although the ancient Hindu mathematician Apastambha had achieved a good approximation for √2, and the ancient Babylonians an ever better √2, neither of these ancient cultures achieved a π approximation as good as Egypt's, or better than π ≈ 25/8, until the Alexandrian era. reference: http://fabpedigree.com/james/mathmen.htm
252
Namaj/Salat / Re: জানাযার নামাজ (পদ্ধতি ও করণীয়)
« on: March 05, 2012, 03:27:13 PM »
very important post
254
Science Discussion Forum / even perfect number
« on: March 05, 2012, 03:23:41 PM »
Over 2300 years ago Euclid proved that If 2^(k)-1 is a prime number (it would be a Mersenne prime), then 2^(k-1)(2^(k)-1) is a perfect number. A few hundred years ago Euler proved the converse (that every even perfect number has this form). It is still unknown if there are any odd perfect numbers (but if there are, they are large and have many prime factors).
255
Science Discussion Forum / Re: How classrooms are becoming 'smart'
« on: March 05, 2012, 03:19:10 PM »
Nice post