# 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, and are respectively the Weierstrass elliptic function, its derivative, and the Weierstrass zeta function, with invariants and , and and are the usual beta and gamma functions. The invariants are the ones corresponding to the semi-periods and . The parameter ranges are and .

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 !!