## Mathematical discovery: on understanding, learning and teaching problem solving, Volume 1 |

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algebra analogous angle Auxiliary figure binomial coefficients binomial theorem chapter clauses compute consider corresponding Descartes desired determine diagonals differential equation distance example express fact foregoing four geometric construction given circle given point Hence Heron's formula integers intersection kind length loci locus magic square mathematical induction method Newton notation obtain particular Pascal triangle pattern perpendicular plane plane geometry polynomial of degree power series prismoid prismoidal formula problem solving problem to find procedure proof proposed problem pyramid radius reader rectangle recursion recursion formula relation respectively result of ex right triangle satisfying sect segment shortest zigzag paths Simpson's rule solid geometry solution of ex special situation split the condition square straight line subset system of equations tangents tetrahedron theorem tion total number triangular upper base values vertex vertices volume word xu x2 yields