"Waymark seekers assume all risks and responsibilities involved in seeking this and any waymark."
Examples of Palindromes
SIMPLE WORDS:
radar
level
civic
kayak
racecar
PHRASES:
Was it a rat I saw
Able was I ere I saw Elba
Go hang a salami I'm a lasagna hog
DATES:
January 2, 2010 (01/02/2010)
November 2, 2011 (11/02/2011)
NUMBERS:
11
292
34543
98765432123456789
Other palindromes can be found in DNA sequences and musical note sequences.
Even art has a form of palindrome called a tessellation, where, for example, the form of a goose flying one way defines the form of a goose flying the opposite way, in a kind of tiled pattern.
COORDINATE PALINDROMES
The object of this waymark category is to find a set of coordinates whose digits read the same forward and backward.
An example palindrome coordinate would be:
N 37° 13.512 W 121° 53.173 (or 371351212153173)
You find a set of coordinates on your own that are a palindrome and visit it. Take a picture or screenshot of your GPSr showing the palindrome coordinates. Take another picture showing the general area where the coordinates can be found. More pictures are always welcome. Create a waymark with the coordinates and your photos to claim a waymark. Include any comments about how you discovered your palindrome, ease or danger in accessing the location, interesting sights or geocaches nearby, and whether permission might be needed to get to the site.
The coordinates may be in any format or datum you wish as long as they are a palindrome. We greatly prefer the default coordinate system of degrees and minutes (MinDec) as displayed in a standard waymark, so it can easily be read. If you choose some other coordinate system or palindrome variant, you must explain in the long description how your numbers form a palindrome, if it does not show in the waymark coordinate display.
COORDINATE PALINDROME ANALYSIS
The prized coordinates are those full palindromes that form a SINGLE number. In those palindromes, the digits of the latitude and longitude influence each other. The beginning digits of the latitude form the final digits of the longitude and vice versa.
Using the coordinate system of degrees and minutes, the standard format for the minutes is MM.MMM. Since this quantity will appear once in both the longitude and latitude, ten digits of the palindrome will come from these numbers. Since latitudes vary from 1 to 2 digits and longitudes vary from 1 to 3 digits, a full palindrome will have another 2 to 5 digits, making palindromes of 12 to 15 digits in total.
If one uses letters to represent the possible digits of a latitude, it can be expressed as:

AB CD.EFG (7 digits), a latitude of two digits (AB) and minutes represented as CD.EFG
or
A CD.EFG (6 digits), in the band near the equator where the latitude (A) is a single digit.

The corresponding palindromic longitude would then be formed, using the same digits in reverse. It can be expressed as:

G FE.DCA (6 digits), in the band near the prime meridian, where longitude (G) is a single digit,
or
GF ED.CBA (7 digits), for longitudes (GF) from 10 to 99 degrees,
or
1GF ED.CBA (8 digits), for longitudes from 100 to 180 degrees and the first digit is always a "1".

The above two combinations for latitude and longitude can be combined to form six different combinations:

The number in parenthesis is the total number of digits in the palindrome. Capital letters in the sequence represent those digits that are fixed by the digits of the longitude and latitude digits. Lowercase letters are those that are variable and have a matching digit in the other component of the coordinates. With 2 digit latitudes, three digits can vary with the c and e digit being limited from 0 to 5, making 360 palindromes per degree confluence (6x6x10).
• 2digit latitude, 3digit longitude: AB cd.eFG, 1GF ed.cBA (15 digits)
A fairly common combination, that will reflect around the digit one of the longitude.
• 2digit latitude, 2digit longitude: AB cd.eFG, GF ed.cBA (14 digits)
(optional leading zero in the longitude, would make it a 15 digit case)
Another combination where the degree value becomes the trailing digits of the other coordinate value.
• 2digit latitude, 1digit longitude: AB cd.eFx, F ed.cBA (13 digits)
This coordinate area is restricted to a band along the prime meridian. What's interesting in these palindromes, is that the final digit of the latitude (center digit of the palindrome) can be any value and still be a palindrome. Thus at each of the usual 360 possible palindrome possibilities, there are 10 palindromes that could be located along the latitude!
With a 1digit latitudes, these palindromes will follow a band along the equator and form a special case. There are four digits that can vary with digits c and f being restricted to 0 to 5 values, making 3600 palindromes per degree confluence (6x6x10x10).
• 1digit latitude, 3digit longitude: A cd.efG, 11G fe.dcA (14 digits)
Because these palindrome have an even number of digits, the three digit longitude is forced to be 11x. At longitude 11x West, palindromes are in the Pacific Ocean, but at 11x East, some palindromes will fall in the Malaysia / Indonesia region.
• 1digit latitude, 2digit longitude: A cd.efG, xG fe.dcA (13 digits)
Two digit longitudes can be found in Africa and South America along the equator. The interesting feature of these odd digit palindromes is that the center digit of the palindrome is the first digit of the longitude, allowing it to take on any value.
• 1digit latitude, 1digit longitude: A cd.efG, G fe.dcA(12 digits)
These short palindromes will be located at the intersection of the band along the equator and the band along the prime meridian. This area is mostly in the south Atlantic Ocean, but the square of intersection does come onshore at the "dent" in Africa on the west coast. This is a somewhat rich area, but mostly in the ocean.

COORDINATE PALINDROME LOCATIONS
Small programs or scripts can be written to iterate through the varying digits and generate the palindrome possibilities for a particular degree confluence region. If anyone would like a list of the coordinate palindromes for a particular latitude/longitude, please send a note to the category manager. These possibilities can then be plotted on a Google map to help locate them. I created a couple of Google maps to investigate the accessibility of the palindromes in my area. You can use the satellite view to drill down and see if the coordinates lie on a house rooftop or some other inaccessible area.
Palindromes with a two digit latitude are found to be arranged on parallel lines on the earth running from NW to SE. These lines are about 10.5 miles apart and the palindrome locations on the lines occur about every 1.45 miles.
Here's a sampling of palindromes plotted on a live Google map for the San Francisco Bay area (N37, W122). Note the interesting arrangement of palindromes in parallel lines.
View San Francisco Palindromes in a larger map
The Google bubbles are colorcoded:
Green bubbles  Accessible
Yellow bubbles  Possibly accessible
Red bubbles  Probably inaccessible, private property, back yards, rooftops or other reasons
Blue bubbles  Over water
If the bubble has a black dot inside, it has been visited to verify its status. The popup balloon from clicking on a green bubble will have a link to the created waymark.
OTHER COORDINATE PALINDROME VARIATIONS
A more common form of coordinate palindrome is the case where each of the latitude and longitude form a small palindrome within them self. These are of the form AB cd.cBA, FG hi.hGF. These will be referred to as dual coordinate palindromes, since there are two separate palindromes. Since the digits of the latitude and longitude do not influence each other, the inner digits of each must form a 3digit palindrome within. Since the first digit of this inner palindrome, c or h is again restricted to 0 to 5, the available combinations result in 60 possible palindromes for each, resulting in 3,600 possible for both in a single degree confluence. Since these palindromes are shorter and more prevalent, they are mundane and will no longer be accepted.
Coordinate palindromes in notations other than DegMin have been posted and have been grandfathered in the category.
WM1F36 is an example where the GPS unit was set to display in Degrees, Minutes and Seconds (DMS) DDMMSS.S, resulting in a dual coordinate palindrome:
N 51° 03' 01.5"
W 114° 00' 41.1"
WMCW2 is an example where the GPS unit was set to display Decimal Degrees (DegDec) DD.DDDDD, resulting in a dual coordinate palindrome:
N 41.50514°
W 090.55090°
WMKVB is an example where the GPS unit was set to display Decimal Degrees (DegDec) DD.DDDDD, and a full coordinate palindrome was found:
N 58.95650 E 005.65985
Other palindromes could be formed by adding a leading zero in the latitude (or possibly even the longitude). These zeros are unnecessary, but are often displayed by GPS units. WM17BA is an example of a full palindrome where the GPS unit was not even displaying the leading zero, technically making this a 16digit palindrome!
No detailed analysis has been done of these coordinate palindrome variations. They will be accepted, since full palindromes are the prized candidates in this category. Variant palindromes are no longer being accepted.