THE MATHEMATICS OF AMERICAN COUSINSHIP

Richard Roark

Two individuals are said to be nth cousins if they are related at
the (n+l)th generation level through a set of (n-I) great grandparents.
(n-i) great grandparents is defined as grandparents for n - 1, and as

great great great . . . (n-l) grandparents for n > 1.  Thus, for n = 3,
(n-l) great grandparents is read great great grandparents.

Two individuals are said to be nth cousins x times removed if one
is the lineal descendant, x generations removed, of an nth cousin of the
other; or conversely, if one is an nth cousin of a lineal ascendant, x
generations removed, of the other.

Thus two nth cousins x times removed are related through a common
male and a common female ancestor who constitute a set of (n-l)(great)

grandparents on the (n+l)th generation level for one cousin, and a set of

n-3+x)(great) grandparents on the (n+l+x)th generation level for the other
cousin.

To determine the relationship between the lineal descendants of two
nth cousins x times removed, let A be the cousin (n+l) generations removed
from the pair of common ancestors and B the other cousin. Let q be the

number of generations between A and his lineal descendant C, and r the num-
ber of generations between B and his lineal descendant D.  Then C and D

will be (n+q)th cousins if q ' (x+r); (n+x+r)th cousins if q > (x+r). In
either case they will be Ix+r-qj times removed. The procedure may be re-
versed to determine the relationship between the lineal ascendants of two
nth cousins x times removed, subject to the restriction that n and x be
positive.

17

American Cousinship

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\ t cO5--r's~COU ind t s 2 . ~

3rd cousins                A-

=60

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1st cousins .. }st cousinso

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q-1 gen.      ~                                       O~C

A                        0           D0

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q 5 (x + r)                            q > (x + r)

(n + q) a 2                           (n + x + r) - h

jx + r - q   12 + 2- 1   3            {x + r - ql    1    - 51  = 1-31 - 3