Costa’s minimal surface and its applicability for $SPX year end projection
incase if you had forgotten the equation from your physics classes .. ,the Costa’s minimal surface equation is below
The other day, we finally managed to apply Alfred Gray’s parametric equations on how to use it for $SPX year end price target.
Here, 
We may not be able to give the full details ( as they are proprietary of nature ) on how to manipulate the Weierstrass elliptic functions that show up in the equations, but below the details on how the equation fared against each year end’s actual $SPX close
| Year | Actual $SPX Close | Equation Prediction | Error in the Prediction |
| 2016 | ?? | 3665 | ?? |
| 2015 | 2044 | 2040 | 0.19 |
| 2014 | 2059 | 2076 | 0.82 |
| 2013 | 1848 | 1858 | 0.52 |
| 2012 | 1426 | 1414 | 0.86 |
| 2011 | 1258 | 1250 | 0.61 |
| 2010 | 1258 | 1248 | 0.77 |
| 2009 | 1115 | 1126 | 0.97 |
| 2008 | 903 | 901 | 0.25 |
| 2007 | 1468 | 1472 | 0.25 |
| 2006 | 1418 | 1406 | 0.87 |
| 2005 | 1248 | 1256 | 0.61 |
| 2004 | 1212 | 1206 | 0.49 |
| 2003 | 1112 | 1108 | 0.35 |
| 2002 | 880 | 885 | 0.59 |
| 2001 | 1148 | 1141 | 0.62 |
| 2000 | 1320 | 1330 | 0.73 |
| 1999 | 1469 | 1456 | 0.91 |
| 1998 | 1229 | 1232 | 0.22 |
| 1997 | 970 | 971 | 0.06 |
| 1996 | 741 | 742 | 0.17 |
| 1995 | 616 | 612 | 0.64 |
| 1994 | 459 | 462 | 0.59 |
| 1993 | 466 | 464 | 0.53 |
| 1992 | 436 | 434 | 0.39 |
| 1991 | 417 | 419 | 0.46 |
| 1990 | 330 | 329 | 0.37 |
| 1989 | 353 | 353 | 0.11 |
| 1988 | 278 | 278 | 0.10 |
| 1987 | 247 | 247 | 0.03 |
| 1986 | 242 | 241 | 0.49 |
| 1985 | 211 | 213 | 0.81 |
| 1984 | 167 | 167 | 0.14 |
| 1983 | 165 | 165 | 0.04 |
| 1982 | 141 | 140 | 0.46 |
| 1981 | 123 | 123 | 0.37 |
| 1980 | 136 | 135 | 0.56 |
| 1979 | 108 | 109 | 0.97 |
| 1978 | 96 | 97 | 0.92 |
| 1977 | 95 | 96 | 0.94 |
| 1976 | 107 | 107 | 0.43 |
| 1975 | 90 | 90 | 0.21 |
| 1974 | 69 | 69 | 0.64 |
| 1973 | 98 | 98 | 0.46 |
| 1972 | 118 | 118 | 0.04 |
| 1971 | 102 | 103 | 0.88 |
| 1970 | 92 | 93 | 0.91 |
| 1969 | 92 | 92 | 0.07 |
| 1968 | 104 | 103 | 0.83 |
| 1967 | 96 | 97 | 0.55 |
| 1966 | 80 | 80 | 0.41 |
| 1965 | 92 | 93 | 0.61 |
| 1964 | 85 | 85 | 0.29 |
| 1963 | 75 | 75 | 0.03 |
| 1962 | 63 | 63 | 0.16 |
| 1961 | 72 | 71 | 0.77 |
| 1960 | 58 | 58 | 0.19 |
| 1959 | 60 | 60 | 0.18 |
| 1958 | 55 | 55 | 0.38 |
| 1957 | 40 | 40 | 0.02 |
| 1956 | 47 | 47 | 0.70 |
| 1955 | 45 | 46 | 1.13 |
| 1954 | 36 | 36 | 0.06 |
| 1953 | 25 | 25 | 0.76 |
| 1952 | 27 | 27 | 1.59 |
| 1951 | 24 | 24 | 0.96 |
| 1950 | 20 | 21 | 2.71 |
ps: you might want to decode 3665 ( which is the year end target ) on your phone !!
