wongwyman0
Oct 20, 2017

G-E-O-ME-TRY

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The problem below on Euclidean Geometry may pose a serious challenge to the mathematically gifted students based on common principles and theorems of plane geometry, in particular, congruency of two triangles.

 

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  • tosophiechen
    Oct 20, 2017

    Another problem is on congruency of triangles to challenge the motivated students in plane geometry.
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    May 4, 2017

    Suppose that we are told that four numbers a , b , c , d lie between -5 and 5. Suppose also that the numbers are constrained so that 5 < a + b < 10 and -10 < c + d < -5 Given this information, what can you deduce about these inequalities? ?? < a + b-c-d < ?? ?? < a-c < ?? ?? < a-c+d-b < ?? ?? < abcd < ?? Did you know ... ? There are many useful general inequalities in mathematics, such as the AM-GM, Cauchy-Schwarz and Jensen's inequalities. These general inequalities are powerful tools which greatly simplify a wide variety of problems in mathematics, in applications from integration to probability via linear algebra.
  • tosophiechen
    May 4, 2017

    Find a solution to this equation to 1 dp. Are there any others? Did you know ... ? Numerical solution of equations forms an important part of real-world mathematics and mathematics applied to science, where equations are often too complex to be solved exactly. Mathematicians have developed many advanced techniques for the numerical solution and exploration of equations.

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