# Costa’s minimal surface equation and its applicability for $SPX year end projection # Costa’s minimal surface and its applicability for$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, $\wp, \wp^\prime$ and $\zeta$ are respectively the Weierstrass elliptic function, its derivative, and the Weierstrass zeta function, with invariants $g_2=\left(\frac12\mathrm{B}\left(\frac14,\frac14\right)\right)^4=\frac{\Gamma(1/4)^8}{16\pi^2}$ and $0$, and $\mathrm{B}(x,y)$ and $\Gamma(x)$ are the usual beta and gamma functions. The invariants are the ones corresponding to the semi-periods $\omega_1=\frac12$ and $\omega_3=\frac{i}{2}$. The parameter ranges are $0 < u < 1$ and $0 < v < 1$. 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 !!