Birthday Triangles

It's my birthday, and I tried to find a puzzle related to it. I was hoping to find that my birth year and the current year (1998) could both be used as two sides of a Pythagorean Triangle (a right triangle with integral sides), but that was not to be. But luckily, I was able to determine that there will come one (and only one) year when my birth year and the current year are two of the sides of such a triangle (I'll be an even age, as I am now, but I'll not yet be 100 years old.)
  1. How old am I today? (I'm not 22.)
  2. What birth year this century can be used in the greatest number of such birthday triangles? (Where the birth year and a greater year within 100 years are both sides of a Pythagorean Triangle.)
  3. What birth year next century?

Source: Original.

Solutions were received from Kirk Bresniker, Alexander Doskey, Denis Borris, Robert McQuaid, Philippe Fondanaiche.

  1. I am 30 years old today (July 27, 1998). The best way to analyze this is as below (thanks to Alexander Doskey for this creating this list): 
    Birth Year      Current Year    Third           Age
1900            1995            2755            95   --more than one triangle
 1900           1972            528             72   --more than one triangle
1904            1920            2704            16   --more than one triangle
 1904           1921            255             17   --more than one triangle
 1904           1940            372             36   --more than one triangle
1911            1961            440             50   --would not be an even age
1914            1930            248             16   --is not a future date
1920            1924            124             4     --more than one triangle
 1920           1952            352             32   --more than one triangle
 1920           1968            432             48   --more than one triangle
 1920           2000            560             80   --more than one triangle
 1920           2016            2784            96   --more than one triangle
1927            1945            264             18   --would not be an even age
1932            1940            176             8     --more than one triangle
 1932           1955            299             23   --more than one triangle
1935            1937            88              2     --would not be an even age
1936            2035            627             99   --would not be an even age
1938            1950            216             12   --is not a future date
1940            2037            2813            97   --would not be an even age
1944            2025            567             81   --would not be an even age
1950            1970            280             20   --is not a future date
1953            2015            496             62   --would not be an even age
1955            2045            600             90   --would not be an even age
1960            2001            2801            41   --more than one triangle
 1960           2009            441             49   --more than one triangle
 1960           2058            2842            98   --more than one triangle
1968            2050            574             82   <------this must be the one
1972            1997            315             25   --would not be an even age
1976            2074            630             98   --admitted you were not 22
1980            1989            189             9     --more than one triangle
 1980           1991            209             11   --more than one triangle
 1980           2013            363             33   --more than one triangle
 1980           2015            2825            35   --more than one triangle
 1980           2020            400             40   --more than one triangle
 1980           2076            624             96   --more than one triangle
 1980           2079            2871            99   --more than one triangle
1984            1985            63              1     --would not be an even age
1989            2061            540             72   --would not be an even age
1992            2075            581             83   --would not be an even age
1995            2005            200             10   --more than one triangle
 1995           2051            476             56   --more than one triangle
1998            2098            640             100 --after this point and you would not yet be born
  2. The most triangles for any year this century is seven for 1980: 
         189     1980     1989
     209     1980     1991
     363     1980     2013
             1980     2015     2825
     400     1980     2020
     624     1980     2076 
             1980     2079     2871
  3. The most triangles for any year the next century is six for 2016: 
         238     2016     2030
     270     2016     2034
     312     2016     2040
     512     2016     2080
     555     2016     2091
     588     2016     2100
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