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Difference between revisions of "User talk:1=2"

(some progress on some random problem, will try to solve in dorms)
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1966 IMO Problem 3 Progress
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It turns out that many contests that are on the AoPSWiki are not formatted correctly. Some examples of articles on a contest formatted correctly is [[2000 AMC 8]], [[2000 AMC 8 Problems]], and [[2000 AMC 8 Problems/Problem 1]]. Below is a list of every single contest in the AMC series, as well as the IMO. If you have time, could you please make sure that these contests are in the right format? Thanks, and feel free to mark contests complete ('''do not delete them, mark them complete''') if they have been completed. Note that not all problems need solutions for the pages to be correctly formatted.
  
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Let the tetrahedron be <math>ABCD</math>, and let the circumcenter be <math>O</math>. Therefore <math>OA=OB=OC=OD</math>. It's not hard to see that <math>O</math> is the intersection of the planes that perpendicularly bisect the six sides of the tetrahedron. Label the plane that bisects <math>AB</math> as <math>p_{AB}</math>, and define <math>p_{AC}</math>, <math>p_{BC}</math>, <math>p_{AD}</math>, <math>p_{BD}</math>, and <math>p_{CD}</math> similarly. Now consider <math>p_{AB}</math>, <math>p_{BC}</math>, and <math>p_{CA}</math>. They perpendicularly bisect three coplanar segments, so their intersection is a line perpendicular to the plane containing <math>ABC</math>. Note that the circumcenter of <math>ABC</math> is on this line.
+
== Articles that may or may not be in the correct format ==
 +
=== AJHSME / AMC 8 ===
 +
* [[1985 AJHSME]]
 +
* [[1986 AJHSME]]
 +
* [[1987 AJHSME]]
 +
* [[1988 AJHSME]]
 +
* [[1989 AJHSME]]
 +
* [[1990 AJHSME]]
 +
* [[1991 AJHSME]]
 +
* [[1992 AJHSME]]
 +
* [[1993 AJHSME]]
 +
* [[1994 AJHSME]]
 +
* [[1995 AJHSME]]
 +
* [[1996 AJHSME]]
 +
* [[1997 AJHSME]]
 +
* [[1998 AJHSME]]
 +
* [[1999 AMC 8]]
 +
* [[2000 AMC 8]]
 +
* [[2001 AMC 8]]
 +
* [[2002 AMC 8]]
 +
* [[2003 AMC 8]]
 +
* [[2004 AMC 8]]
 +
* [[2005 AMC 8]]
 +
* [[2006 AMC 8]]
 +
* [[2007 AMC 8]]
 +
* [[2008 AMC 8]]
 +
* [[2009 AMC 8]]
 +
* [[2010 AMC 8]]
  
−
**solving easier version**
+
=== AMC 10 ===
 +
* [[2000 AMC 10]]
 +
* [[2001 AMC 10]]
 +
* [[2002 AMC 10A]]
 +
* [[2002 AMC 10B]]
 +
* [[2003 AMC 10A]]
 +
* [[2003 AMC 10B]]
 +
* [[2004 AMC 10A]]
 +
* [[2004 AMC 10B]]
 +
* [[2005 AMC 10A]]
 +
* [[2005 AMC 10B]]
 +
* [[2006 AMC 10A]]
 +
* [[2006 AMC 10B]]
 +
* [[2007 AMC 10A]]
 +
* [[2007 AMC 10B]]
 +
* [[2008 AMC 10A]]
 +
* [[2008 AMC 10B]]
 +
* [[2009 AMC 10A]]
 +
* [[2009 AMC 10B]]
 +
* [[2010 AMC 10A]]
 +
* [[2010 AMC 10B]]
 +
* [[2011 AMC 10A]]
 +
* [[2011 AMC 10B]]
  
−
I shall prove that given triangle <math>ABC</math>, the minimum value of <math>PA+PB+PC</math> is given when <math>P</math> is the circumcenter of <math>ABC</math>. It's easy to see that, from the Pythagorean Theorem, that if <math>P</math> is not on the plane containing <math>ABC</math>, then the projection <math>P'</math> of <math>P</math> onto said plane satisfies
 
  
−
<cmath>P'A+P'B+P'C<PA+PB+PC</cmath>
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=== AHSME / AMC 12 ===
  
−
so it suffices to consider all points <math>P</math> that are coplanar with <math>ABC</math>.
+
* [[1951 AHSME]]
 +
* [[1952 AHSME]]
 +
* [[1953 AHSME]]
 +
* [[1954 AHSME]]
 +
* [[1955 AHSME]]
 +
* [[1956 AHSME]]
 +
* [[1957 AHSME]]
 +
* [[1958 AHSME]]
 +
* [[1959 AHSME]]
 +
* [[1960 AHSME]]
 +
* [[1961 AHSME]]
 +
* [[1962 AHSME]]
 +
* [[1963 AHSME]]
 +
* [[1964 AHSME]]
 +
* [[1965 AHSME]]
 +
* [[1966 AHSME]]
 +
* [[1970 AHSME]]
 +
* [[1993 AHSME]]
 +
* [[2000 AMC 12]]
 +
* [[2001 AMC 12]]
 +
* [[2002 AMC 12A]]
 +
* [[2002 AMC 12B]]
 +
* [[2003 AMC 12A]]
 +
* [[2003 AMC 12B]]
 +
* [[2004 AMC 12A]]
 +
* [[2004 AMC 12B]]
 +
* [[2005 AMC 12A]]
 +
* [[2005 AMC 12B]]
 +
* [[2006 AMC 12A]]
 +
* [[2006 AMC 12B]]
 +
* [[2007 AMC 12A]]
 +
* [[2007 AMC 12B]]
 +
* [[2008 AMC 12A]]
 +
* [[2008 AMC 12B]]
 +
* [[2009 AMC 12A]]
 +
* [[2009 AMC 12B]]
 +
* [[2010 AMC 12A]]
 +
* [[2010 AMC 12B]]
 +
* [[2011 AMC 12A]]
 +
* [[2011 AMC 12B]]
 +
 
 +
=== AIME ===
 +
 
 +
* [[1983 AIME]]
 +
* [[1984 AIME]]
 +
* [[1985 AIME]]
 +
* [[1986 AIME]]
 +
* [[1987 AIME]]
 +
* [[1988 AIME]]
 +
* [[1989 AIME]]
 +
* [[1990 AIME]]
 +
* [[1991 AIME]]
 +
* [[1992 AIME]]
 +
* [[1993 AIME]]
 +
* [[1994 AIME]]
 +
* [[1995 AIME]]
 +
* [[1996 AIME]]
 +
* [[1997 AIME]]
 +
* [[1998 AIME]]
 +
* [[1999 AIME]]
 +
* [[2000 AIME I]]
 +
* [[2000 AIME II]]
 +
* [[2001 AIME I]]
 +
* [[2001 AIME II]]
 +
* [[2002 AIME I]]
 +
* [[2002 AIME II]]
 +
* [[2003 AIME I]]
 +
* [[2003 AIME II]]
 +
* [[2004 AIME I]]
 +
* [[2004 AIME II]]
 +
* [[2005 AIME I]]
 +
* [[2005 AIME II]]
 +
* [[2006 AIME I]]
 +
* [[2006 AIME II]]
 +
* [[2007 AIME I]]
 +
* [[2007 AIME II]]
 +
* [[2008 AIME I]]
 +
* [[2008 AIME II]]
 +
* [[2009 AIME I]]
 +
* [[2009 AIME II]]
 +
* [[2010 AIME I]]
 +
* [[2010 AIME II]]
 +
* [[2011 AIME I]]
 +
* [[2011 AIME II]]
 +
 
 +
=== USAMO ===
 +
 
 +
*[[1972 USAMO]]
 +
*[[1973 USAMO]]
 +
*[[1974 USAMO]]
 +
*[[1975 USAMO]]
 +
*[[1976 USAMO]]
 +
*[[1977 USAMO]]
 +
*[[1978 USAMO]]
 +
*[[1979 USAMO]]
 +
*[[1980 USAMO]]
 +
*[[1981 USAMO]]
 +
*[[1982 USAMO]]
 +
*[[1983 USAMO]]
 +
*[[1984 USAMO]]
 +
*[[1985 USAMO]]
 +
*[[1986 USAMO]]
 +
*[[1987 USAMO]]
 +
*[[1988 USAMO]]
 +
*[[1989 USAMO]]
 +
*[[1990 USAMO]]
 +
*[[1991 USAMO]]
 +
*[[1992 USAMO]]
 +
*[[1993 USAMO]]
 +
*[[1994 USAMO]]
 +
*[[1995 USAMO]]
 +
*[[1996 USAMO]]
 +
*[[1997 USAMO]]
 +
*[[1998 USAMO]]
 +
*[[1999 USAMO]]
 +
*[[2000 USAMO]]
 +
*[[2001 USAMO]]
 +
*[[2002 USAMO]]
 +
*[[2003 USAMO]]
 +
*[[2004 USAMO]]
 +
*[[2005 USAMO]]
 +
*[[2006 USAMO]]
 +
*[[2007 USAMO]]
 +
*[[2008 USAMO]]
 +
*[[2009 USAMO]]
 +
*[[2010 USAMO]]
 +
*[[2011 USAMO]]
 +
 
 +
=== IMO ===
 +
* [[1959 IMO]]
 +
* [[1960 IMO]]
 +
* [[1961 IMO]]
 +
* [[1962 IMO]]
 +
* [[1963 IMO]]
 +
* [[1964 IMO]]
 +
* [[1965 IMO]]
 +
* [[1966 IMO]]
 +
* [[1967 IMO]]
 +
* [[1968 IMO]]
 +
* [[1969 IMO]]
 +
* [[1970 IMO]]
 +
* [[1971 IMO]]
 +
* [[1972 IMO]]
 +
* [[1973 IMO]]
 +
* [[1974 IMO]]
 +
* [[1975 IMO]]
 +
* [[1976 IMO]]
 +
* [[1977 IMO]]
 +
* [[1978 IMO]]
 +
* [[1979 IMO]]
 +
* [[1980 IMO]]
 +
* [[1981 IMO]]
 +
* [[1982 IMO]]
 +
* [[1983 IMO]]
 +
* [[1984 IMO]]
 +
* [[1985 IMO]]
 +
* [[1986 IMO]]
 +
* [[1987 IMO]]
 +
* [[1988 IMO]]
 +
* [[1989 IMO]]
 +
* [[1990 IMO]]
 +
* [[1991 IMO]]
 +
* [[1992 IMO]]
 +
* [[1993 IMO]]
 +
* [[1994 IMO]]
 +
* [[1995 IMO]]
 +
* [[1996 IMO]]
 +
* [[1997 IMO]]
 +
* [[1998 IMO]]
 +
* [[1999 IMO]]
 +
* [[2000 IMO]]
 +
* [[2001 IMO]]
 +
* [[2002 IMO]]
 +
* [[2003 IMO]]
 +
* [[2004 IMO]]
 +
* [[2005 IMO]]
 +
* [[2006 IMO]]
 +
* [[2007 IMO]]
 +
* [[2008 IMO]]
 +
* [[2009 IMO]]
 +
* [[2010 IMO]]
 +
* [[2011 IMO]]

Revision as of 14:55, 19 July 2011

It turns out that many contests that are on the AoPSWiki are not formatted correctly. Some examples of articles on a contest formatted correctly is 2000 AMC 8, 2000 AMC 8 Problems, and 2000 AMC 8 Problems/Problem 1. Below is a list of every single contest in the AMC series, as well as the IMO. If you have time, could you please make sure that these contests are in the right format? Thanks, and feel free to mark contests complete (do not delete them, mark them complete) if they have been completed. Note that not all problems need solutions for the pages to be correctly formatted.

Articles that may or may not be in the correct format

AJHSME / AMC 8

AMC 10


AHSME / AMC 12

AIME

USAMO

IMO

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