radian (noun): An invented word based on radius (q.v.); in a circle, a radian is the size of a central angle subtended by an arc equal in length to the radius of the circle. The earliest use of radian recorded in the Oxford English Dictionary dates back only as far as 1879. Radian measure has also been called circular measure, and on rare occasions π measure and natural measure. [177]

radical (noun): from Latin radix, stem radic- “root,” from the Indo-European root wrad- “branch, root.” An English cognate of radix is root, borrowed from Old Norse. A radical reformer wants to get to the root of social problems, often by means considered extreme; as a consequence, any extremist may now be called a radical. In differentwords, a radical wants to eradicate society's ills by pulling them up the roots. In algebra the radical symbol, indicates that the nth root of a quantity is being taken. The symbol itself is abstracted from the first letter of Latin radix. For quite some time the symbol was used without a horizontal bar at the top. The current version of the symbol is actually a fusion of the stylized letter r and the vinculum (q.v.) that was later used when a sum of terms was to have its root extracted. Some students mistakenly think a radical always involves a square root, probably because a square root is almost always indicated by a radical without an explicit index.