The dram (archaic spelling drachm; apothecary symbol ℨ) was historically both a coin and a weight.
In the avoirdupois system, the dram is the mass of
1⁄256 pound or
1⁄16 ounce.
So the dram weighs 875⁄32 grains or exactly 1.771 845 195 3125 grams.
The dram (symbol: ʒ) is also the mass of 1⁄96 pound (℔) or 1⁄8 ounce (℥) in the apothecaries' system that survived until the middle of the 20th century in English-speaking countries. It is equal to 3 scruples (℈) or 60 grains (G). Thus, it is equal to exactly 3.887 9346 grams.
The fluid dram is defined as 1⁄8 of a fluid ounce, which means it is exactly equal to
In the United Kingdom, a teaspoon was formerly defined as 3/2 fluid dram.
Dram is also used informally to mean a small amount of liquid, especially Scotch whisky.
MINA
The mina (also mna, Ancient Greek μνᾶ) is an ancient Near Eastern unit of weight equivalent to 50 shekels. The mina, like the shekel, was also a unit of currency; in ancient Greece it was equal to 100 drachmae. The Greek word mna was borrowed from Semitic; compare Hebrew māneh, Aramaic mĕnē, Syriac manyā, Ugaritic mn, and Akkadian manū.
From earliest Sumerian times, a mina was a unit of weight. At first, talents and shekels had not yet been introduced. By the time of Ur-Nammu, the mina had a value of 1/60 talents as well as 60 shekels. The value of the mina is calculated at 1.25 pounds
Ezekiel refers to a mina ('maneh' in the King James Version) as sixty shekels[4].|
Mina of Chios. |
Mina of Antiochus IV Epiphanes. |
Mina of Antioch. |
hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle.
If k is a rational number, say k = p/q expressed in simplest terms, then the curve has p cusps.
If k is an irrational number, then the curve never closes, and fills the space between the larger circle and a circle of radius R − 2r.
|
k=3 - a deltoid |
k=4 - an astroid |
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The hypocycloid is a special kind of hypotrochoid, which are a particular kind of roulette.
A hypocycloid with three cusps is known as a deltoid.
A hypocycloid curve with four cusps is known as an astroid.
The evolute of a hypocycloid is an enlarged version of the hypocycloid itself, while the involute of a hypocycloid is a reduced copy of itself.
The pedal of a hypocycloid with pole at the center of the hypocycloid is a rose curve.
The isoptic of a hypocycloid is a hypocycloid.
The ellipse (drawn in red) may be expressed as a special case of the hypotrochoid, with R = 2r; here R = 10, r = 5, d = 1.
The red curve is a hypotrochoid drawn as the smaller black circle rolls around inside the larger blue circle (parameters are R = 5.0, r = 3, d = 5).



In mathematics, the n-th cabtaxi number, typically denoted Cabtaxi(n), is defined as the smallest positive integer that can be written as the sum of two positive or negative or 0 cubes in n ways. Such numbers exist for all n (since taxicab numbers exist for all n); however, only 10 are known (sequence A047696 in OEIS):





one SQUARE = one 10 SQARED = 100thousand SQUARED = Million ~ZEROS6 ~1 illi on Million SQUARED = Trillion ~ ZEROS12 ~ 3 illi on Trillion SQUARED = septillion ~ ZEROS 24 ~ 7 illi on septillionSQ = quindecillion ~ ZEROS 48 ~ 15 illi on Number of zeros | ||
| 3 | thousand | |
| 6 | million | |
| 9 | billion | |
| 12 | trillion | |
| 15 | quadrillion | |
| 18 | quintillion | |
| 21 | sextillion | |
| 24 | septillion | |
| 27 | octillion | |
| 30 | nonillion | |
| 33 | decillion | |
| 36 | undecillion | |
| 39 | duodecillion | |
| 42 | tredecillion | |
| 45 | quattuordecillion | |
| 48 | quindecillion | |
| 51 | sexdecillion | |
| 54 | septendecillion | |
| 57 | octodecillion | |
| 60 | novemdecillion | |
| 63 | vigintillion | |
| 66 - 120 | ||
| 303 | centillion | |
| 600 |