9
Circa 300 BC, as part of the Brahmi numerals, various Indians wrote a digit 9 similar in shape to the modern closing question mark without the bottom dot. The Kshatrapa, Andhra and Gupta started curving the bottom vertical line coming up with a 3-look-alike.[1] How the numbers got to their Gupta form is open to considerable debate. The Nagari continued the bottom stroke to make a circle and enclose the 3-look-alike, in much the same way that the sign @ encircles a lowercase a. As time went on, the enclosing circle became bigger and its line continued beyond the circle downwards, as the 3-look-alike became smaller. Soon, all that was left of the 3-look-alike was a squiggle. The Arabs simply connected that squiggle to the downward stroke at the middle and subsequent European change was purely cosmetic.
While the shape of the glyph for the digit 9 has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in 
.
The modern digit resembles an inverted 6. To disambiguate the two on objects and labels that can be inverted, they are often underlined. It is sometimes handwritten with two strokes and a straight stem, resembling a raised lower-case letter q, which distinguishes it from the 6. Similarly, in seven-segment display, the number 9 can be constructed either with a hook at the end of its stem or without one. Most LCD calculators use the former, but some VFD models use the latter.
Nine is the fourth composite number, and the first composite number that is odd. Nine is the third square number (32), and the second non-unitary square prime of the form p2, and, the first that is odd, with all subsequent squares of this form odd as well. Nine has the even aliquot sum of 4, and with a composite number sequence of two (9, 4, 3, 1, 0) within the 3-aliquot tree. It is the first member of the first cluster of two semiprimes (9, 10), preceding (14, 15).[2] Casting out nines is a quick way of testing the calculations of sums, differences, products, and quotients of integers in decimal, a method known as long ago as the 12th century.[3]
By Mihăilescu's theorem, 9 is the only positive perfect power that is one more than another positive perfect power, since the square of 3 is one more than the cube of 2.[4][5]
9 is the sum of the cubes of the first two non-zero positive integers which makes it the first cube-sum number greater than one.[6]
