A complex root of unity is called primitive if it has order n. Equivalenly, a is a primitive complex root of unity if and only if an=1 but ar is not 1, for any smaller positive r.

It's quite easy to show that they are exactly: e(2pik/n) with 1<=r<=n and such that r and n have no common factor.

Thus, there are phi(n) primitive roots of unity, where phi is the Euler Phi function.

# KANJI: GEN hara (primitive, original, meadow, field, plain)

#### ASCII Art Representation:

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```

#### Character Etymology:

The radical that surrounds two sides of the character is the radical for cliff while the radical inside is a variant of spring (the watery kind). Thus, cliffside spring, and by extension source/origin and primary/primitive/natural/plain/moor.

#### A Listing of All On-Yomi and Kun-Yomi Readings:

on-yomi: GEN
kun-yomi: hara

Nanori: ta baru ra wata wara

#### English Definitions:

1. GEN: original, primitive.
2. hara: field; plain, prairie, tundra, moor, wilderness.
3. hara(ppa): plain.
4. gen-: original, primitive, primary, fundamental; raw.

New Nelson: 652
Henshall: 107

#### Unicode Encoded Compound Examples:

(genjin): primitive man.
(genbun): original text.

(genshi): atom.
(gensuibaku): atom and hydrogen bombs.

A primitive is a term used in computational geometry to denote one of several basic geometric shapes, such as a cube, ellipsoid, sphere or triangle. When using a ray tracer, typically many world objects are defined in terms of simple primitives, for which ray-object intersection formulas are easy to derive and implement in software. Other interesting shapes can often be described through a constructive solid geometry (CSG) approach to combining primitives.

Prim"i*tive (?), a. [L. primitivus, fr. primus the first: cf. F. primitif. See Prime, a.]

1.

Of or pertaining to the beginning or origin, or to early times; original; primordial; primeval; first; as, primitive innocence; the primitive church.

"Our primitive great sire."

Milton.

2.

Of or pertaining to a former time; old-fashioned; characterized by simplicity; as, a primitive style of dress.

3.

Original; primary; radical; not derived; as, primitive verb in grammar.

Primitive axes of coordinate Geom., that system of axes to which the points of a magnitude are first referred, with reference to a second set or system, to which they are afterward referred. -- Primitive chord Mus., that chord, the lowest note of which is of the same literal denomination as the fundamental base of the harmony; -- opposed to derivative. Moore (Encyc. of Music). -- Primitive circle Spherical Projection, the circle cut from the sphere to be projected, by the primitive plane. -- Primitive colors Paint., primary colors. See under Color. -- Primitive Fathers Eccl., the acknowledged Christian writers who flourished before the Council of Nice, A. D. 325. Shipley. -- Primitive groove Anat., a depression or groove in the epiblast of the primitive streak. It is not connected with the medullary groove, which appears later and in front of it. -- Primitive plane Spherical Projection, the plane upon which the projections are made, generally coinciding with some principal circle of the sphere, as the equator or a meridian. -- Primitive rocks Geol., primary rocks. See under Primary. -- Primitive sheath. Anat. See Neurilemma. -- Primitive streaktrace Anat., an opaque and thickened band where the mesoblast first appears in the vertebrate blastoderm.

Syn. -- First; original; radical; pristine; ancient; primeval; antiquated; old-fashioned.

Prim"i*tive, n.

An original or primary word; a word not derived from another; -- opposed to derivative.