BLOG DO ENG. ARMANDO CAVERO MIRANDA -BRASIL


MACHUPICHU MARAVILHA DO MUNDO

"Two things are infinite: the universe and human stupidity; and I'm not sure about the the universe." ALBERT EINSTEIN - “SE SEUS PROJETOS FOREM PARA UM ANO,SEMEIE O GRÂO.SE FOREM PARA DEZ ANOS,PLANTE UMA ÁRVORE.SE FOREM PARA CEM ANOS,EDUQUE O POVO.” "MATH IS POWER TO CHANGE THE WORLD AND THE KEY TO THE FUTURE" 'OBRIGADO DEUS PELA VIDA,PELA MINHA FAMILIA,PELO TRABALHO,PELO PÃO DE CADA DIA,PROTEGENOS E GUARDANOS DE TODO MAL"

quinta-feira, 16 de agosto de 2012

KAIST Math Problem of the Week

SOURCE WEBSITE:
http://mathsci.kaist.ac.kr/pow/

Concluding 2012 Spring

Thanks all for participating POW actively. Here’s the list of winners:
  • 1st prize: Park, Minjae (박민재) – 2011학번
  • 2nd prize: Lee, Myeongjae  (이명재) – 2012학번
  • 3rd prize: Suh, Gee Won (서기원) – 수리과학과 2009학번
  • 4th prize: Cho, Junyoung (조준영) – 2012학번
  • 5th prize: Kim, Taeho (김태호) – 수리과학과 2011학번
Congratulations! As announced earlier, we have nicer prize this semester – iPad 16GB for the 1st prize, iPod Touch 32GB for the 2nd prize, etc.
KAIST Math Problem of the Week 2012 봄 시상식 박민재 이명재 서기원 조준영 김태호
Posted in annoncement | Tagged , , , , | 2 Comments

Solution: 2012-12 Big partial sum

Let A be a finite set of complex numbers. Prove that there exists a subset B of A such that
zBz1πzAz.
The best solution was submitted by Minjae Park (박민재), 2011학번. Congratulations!
Here is Solution of Problem 2012-12.
Two incorrect solutions were submitted (M.J.L., W.S.J.).
Posted in solution | Tagged | 1 Comment

Solution: 2012-11 Dividing a circle

Let f be a continuous function from [0,1] such that f([0,1]) is a circle. Prove that there exists two closed intervals I1,I2[0,1] such that I1I2 has at most one point, f(I1) and f(I2) are semicircles, and f(I1)f(I2) is a circle.
The best solution was submitted by Myeongjae Lee (이명재), 2012학번. Congratulations!
Here is his Solution of Problem 2012-11.
Alternative solution was submitted by 박민재(2011학번, +3). Two incorrect solutions were submitted (W.S.J., K.M.P.).
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    2012-13 functions for an inequality

    Determine all nonnegative functions f(x,y) and g(x,y) such that
    (i=1naibi)2(i=1nf(ai,bi))(i=1ng(ai,bi))(i=1na2i)(i=1nb2i)
    for all reals ai, bi and all positive integers n.
    Rating: 4.5/5 (13 votes cast)
      Posted in problem | Tagged , , | Leave a comment

      2012-12 Big partial sum

      Let A be a finite set of complex numbers. Prove that there exists a subset B of A such that
      zBz1πzAz.
      Rating: 4.5/5 (14 votes cast)
        Posted in problem | Tagged , | 1 Comment

        Solution: 2012-10 Platonic solids

        Determine all Platonic solids that can be drawn with the property that all of its vertices are rational points.
        The best solution was submitted by Myeongjae Lee (이명재), 2012학번. Congratulations!
        Here is his Solution of Problem 2012-10.
        Alternative solutions were submitted by 박민재 (2011학번, +3, Solution), 정우석 (서강대학교 2011학번, +3), 박훈민 (대전과학고 2학년, +2). One incorrect solution was submitted (G.S.).

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