yielding:
One can check that the quantity
equals 1 if yy = 00 and c ≠ 0, and zero in every other
case. Rewriting steps 1 and 2 from the above algorithm, we have:
January 1 of year mcyy falls on day number
where ε is 1 if the year is a turn of the century, but not the turn of a millennium, and
zero otherwise.
Thus, for example, consider New Year’s Day of the
year 3261. The millennium number here is m = 3, the
century number is c = 2, and we have yy = 61. Also,
, and, since this is not a turn of the
century, ε = 0. Thus New Year’s Day of this year will
fall on day 2 + (2 × 3) – (2 × 2) + 61 + 16 + 0 ≡ 4, a
Thursday. We can now compute the weekday of any
other day that year if we wish.
An Alternative Method
Mathematician Chris McManus has observed that whatever day of the week “March 0” (the last day of February) falls, so do 4/4 (April 4), 6/6 (June 6), 8/8 (August
8), 10/10 (October 10), and 12/12 (December 12). The
same is true of 9/5 (September 5) and 7/11 (July 11), and
their inverses 5/9 and 11/7. (One can remember this
with the mnemonic, “I work from 9 to 5 at the 7-to-11
store.”) So, for example, if you know that December 20,
2002, was a Friday, and you wish to determine the day
on which April 10 of that year fell, quickly compute that
December 12 was a Thursday, yielding April 4 also as a
Thursday, making April 10 a Wednesday.
decibel Denoted dB, a decibel is a measure of the
intensity of sound, with zero decibels representing the
lowest intensity at which a sound can be heard.
Decibels follow a base-10 LOGARITHMIC SCALE.
This means that each increase of 1 dB represents a 10fold increase in the intensity of the sound. For example,
a note played at 1 dB is 10 times as strong as the softest sound, and one played at 2 dB is 100 times as
strong as the softest sound. Normal human speech is at
a level of about 60 dB, and a whisper is around 20 dB.
The threshold of pain for the human ear is about 90
dB. Rock concerts have been known to reach levels of
120 dB at a distance of 50 m from the sound system.
The decibel level of a sound is computed by the
formula:
where P is the intensity of the note being played, and P 0
is the lowest intensity at which that note can be heard.
An interval of 10 dB is called a bel. Sound intensity was originally measured in terms of bel, the name
being chosen in honor of the American inventor of the
telephone, Alexander Graham Bell. Today, however,
the unit of a decibel is considered more useful and
is the one most commonly used.
decimal representation See BASE OF A NUMBER
SYSTEM.
decomposition (factorization) The result of expressing a given object or quantity in terms of simpler components is called a decomposition. For example, the
FUNDAMENTAL THEOREM OF ARITHMETIC shows that
any natural number decomposes as a product of prime
10 10
0
log
P
P
61
4
15 25 16
=
=
.
2 2
2
4
+
− + +
+
m c yy
yy ε
c
yy
yy
10 1000
100
+
−
N L N
N
N
N
m c yy
yy
c
yy
yy
+ = +
−
+
=
− + +
+
+
−
4
100
1000
2
2
4
10 1000
100
.
N
m
c yy m c yy
N
m
c
yy
m c
yy
N
m c
yy
m c
yy
N
m
c
yy
=
+
+ ≡
+ +
=
+
+
≡
+ +
=
+ +
≡
+ +
= +
+
1000
100
6
2
4
250
25
4
5
4
4
100
10
100
3
100
1000
10 1000
118 decibel
One can check that the quantity
equals 1 if yy = 00 and c ≠ 0, and zero in every other
case. Rewriting steps 1 and 2 from the above algorithm, we have:
January 1 of year mcyy falls on day number
where ε is 1 if the year is a turn of the century, but not the turn of a millennium, and
zero otherwise.
Thus, for example, consider New Year’s Day of the
year 3261. The millennium number here is m = 3, the
century number is c = 2, and we have yy = 61. Also,
, and, since this is not a turn of the
century, ε = 0. Thus New Year’s Day of this year will
fall on day 2 + (2 × 3) – (2 × 2) + 61 + 16 + 0 ≡ 4, a
Thursday. We can now compute the weekday of any
other day that year if we wish.
An Alternative Method
Mathematician Chris McManus has observed that whatever day of the week “March 0” (the last day of February) falls, so do 4/4 (April 4), 6/6 (June 6), 8/8 (August
8), 10/10 (October 10), and 12/12 (December 12). The
same is true of 9/5 (September 5) and 7/11 (July 11), and
their inverses 5/9 and 11/7. (One can remember this
with the mnemonic, “I work from 9 to 5 at the 7-to-11
store.”) So, for example, if you know that December 20,
2002, was a Friday, and you wish to determine the day
on which April 10 of that year fell, quickly compute that
December 12 was a Thursday, yielding April 4 also as a
Thursday, making April 10 a Wednesday.
decibel Denoted dB, a decibel is a measure of the
intensity of sound, with zero decibels representing the
lowest intensity at which a sound can be heard.
Decibels follow a base-10 LOGARITHMIC SCALE.
This means that each increase of 1 dB represents a 10fold increase in the intensity of the sound. For example,
a note played at 1 dB is 10 times as strong as the softest sound, and one played at 2 dB is 100 times as
strong as the softest sound. Normal human speech is at
a level of about 60 dB, and a whisper is around 20 dB.
The threshold of pain for the human ear is about 90
dB. Rock concerts have been known to reach levels of
120 dB at a distance of 50 m from the sound system.
The decibel level of a sound is computed by the
formula:
where P is the intensity of the note being played, and P 0
is the lowest intensity at which that note can be heard.
An interval of 10 dB is called a bel. Sound intensity was originally measured in terms of bel, the name
being chosen in honor of the American inventor of the
telephone, Alexander Graham Bell. Today, however,
the unit of a decibel is considered more useful and
is the one most commonly used.
decimal representation See BASE OF A NUMBER
SYSTEM.
decomposition (factorization) The result of expressing a given object or quantity in terms of simpler components is called a decomposition. For example, the
FUNDAMENTAL THEOREM OF ARITHMETIC shows that
any natural number decomposes as a product of prime
10 10
0
log
P
P
61
4
15 25 16
=
=
.
2 2
2
4
+
− + +
+
m c yy
yy ε
c
yy
yy
10 1000
100
+
−
N L N
N
N
N
m c yy
yy
c
yy
yy
+ = +
−
+
=
− + +
+
+
−
4
100
1000
2
2
4
10 1000
100
.
N
m
c yy m c yy
N
m
c
yy
m c
yy
N
m c
yy
m c
yy
N
m
c
yy
=
+
+ ≡
+ +
=
+
+
≡
+ +
=
+ +
≡
+ +
= +
+
1000
100
6
2
4
250
25
4
5
4
4
100
10
100
3
100
1000
10 1000
118 decibel