In zeller's congruence method, what does the z-index stand for?

answer:

zeller's congruence is an algorithm devised by christian zeller to calculate the day of the week for any julian or gregorian calendar date. it can be considered to be based on the conversion between julian day and the calendar date.

step-by-step explanation:

for the gregorian calendar, zeller's congruence is

{\displaystyle h=\left(q+\left\lfloor {\frac {13(m+1)}{5}}\right\rfloor +k+\left\lfloor {\frac {k}{4}}\right\rfloor +\left\lfloor {\frac {j}{4}}\right\rfloor -2j\right){\bmod {7}},}{\displaystyle h=\left(q+\left\lfloor {\frac {13(m+1)}{5}}\right\rfloor +k+\left\lfloor {\frac {k}{4}}\right\rfloor +\left\lfloor {\frac {j}{4}}\right\rfloor -2j\right){\bmod {7}},}

for the julian calendar it is

{\displaystyle h=\left(q+\left\lfloor {\frac {13(m+1)}{5}}\right\rfloor +k+\left\lfloor {\frac {k}{4}}\right\rfloor +5-j\right){\bmod {7}},}{\displaystyle h=\left(q+\left\lfloor {\frac {13(m+1)}{5}}\right\rfloor +k+\left\lfloor {\frac {k}{4}}\right\rfloor +5-j\right){\bmod {7}},}

where

h is the day of the week (0 = saturday, 1 = sunday, 2 = monday, 6 = friday)

q is the day of the month

m is the month (3 = march, 4 = april, 5 = may, 14 = february)

k the year of the century ({\displaystyle year{\bmod {1}}00}{\displaystyle year{\bmod {1}}00}).

j is the zero-based century (actually {\displaystyle \lfloor year/100\rfloor }\lfloor year/100\rfloor ) for example, the zero-based centuries for 1995 and 2000 are 19 and 20 respectively (to not be confused with the common ordinal century enumeration which indicates 20th for both cases).

{\displaystyle \lfloor }{\displaystyle \lfloor } is the floor function or integer part

mod is the modulo operation or remainder after division

m a t h w a y. c o m

step-by-step explanation: