自然数幂和公式与三角公式的几何证明——数学史与数学教学关系个案研究

Intuitive Proofs of the Trigonometric Formulas and Formulas for the Sum of the Powers of Natural Numbers

作为数学教育改革的一种尝试，文章将数学发展的历史与数学教育相结合，给出了自然数幂和公式与三角公式的直观证明．由此探讨了数学史与数学教育的关系（ＨＰＭ）．认为数学史上许多思想方法十分精彩，富有启发性，若能将它们渗透到数学教学中，对数学教育改革将具有极其重要的意义．

Giving intuitive proofs of the trigonometric formulas and formulas for the sum of the powers of natural numbers, which are brief, clear and beautiful, this paper attempts to connect the history with the pedagogy of mathematics and to probe into their relation(HPM for brevity). Many historical methods in mathematics, which, more often than not, are intuitive, wonderful and instruc- tive, can greatly interest the students and activate their thinking and creative ability, if they are taught in mathematics classroom. Therefore, the study of HPM is of great significance for the reform of mathematics instruction.