数学教育学报Issue(5)：1-3,3.
微积分让数据说话
Calculus:Data’s Apology
摘要
Abstract
Calculus can be unified by a philosophical formula with a quantitative ratio:0.9 truthAbsolute truthRelative =0.9. Why? Because calculus is attributed to computing the heights of curves (See the figure 4 in the paper), where a small triangle (Relative truth) replaces a small curved triangle (Absolute truth), and the ratio, Small Height alDifferenti , is used to measure the local error. This procedure goes ahead repeatedly until the sum of differentials replaces the full-height;and then, the ratio, the full-height alsthe sum of differenti , is used to measure the global error. We can observe whether the ratio is closer and closer to 1 (It just means whether Relative truth coincides with Absolute truth). From the experimental data, we found:Small Height alDifferenti =0.999..., the full-height alsthe sum of differenti =0.999... When the partition is refined, there are more 9 in the end of the figure. The repetition leads to an infinite decimal, 0.9, and a unified ratio formula:truthAbsolute truthRelative=0.999...... What an ingenious calculation! The two ratios can be rewritten as Scant Slope SlopeTangent=0.999..., the integral alsthe sum of differenti =0.999... .关键词
微积分/相对真理/绝对真理/比例/0.9Key words
calculus/relative truth/absolute truth/ratio/0.9分类
社会科学引用本文复制引用
林群..微积分让数据说话[J].数学教育学报,2013,(5):1-3,3.基金项目
国家自然科学基金 （）
