论文标题
通过微积分的欧几里得几何学定理
Theorems of Euclidean Geometry through Calculus
论文作者
论文摘要
我们重新启发了Thales，Pythagoras，Apollonius，Stewart，Heron，Al Kashi，de Gua，de Gua，de gua，terquem，terquem，ptolemy，ptolemem，brahmagupta和Euler的定理以及始终的角度定理，辛斯（Sines）的法律，偏见和某些角度，并在某种程度上相互作用。危险中的数量，观察这种关系在这些数量的小偏差下的表现，并自然建立我们整合的微分方程。将一般解决方案应用于某些特定情况，给出了与预期定理相对应的特定解决方案。我们还建立了多项式方程与一组部分微分方程之间的等价性。我们最终评论了一个微小方程，该方程是在小规模转换之后产生的，应涉及度量量之间的所有关系。
We re-derive Thales, Pythagoras, Apollonius, Stewart, Heron, al Kashi, de Gua, Terquem, Ptolemy, Brahmagupta and Euler's theorems as well as the inscribed angle theorem, the law of sines, the circumradius, inradius and some angle bisector formulae, by assuming the existence of an unknown relation between the geometric quantities at stake, observing how the relation behaves under small deviations of those quantities, and naturally establishing differential equations that we integrate out. Applying the general solution to some specific situation gives a particular solution corresponding to the expected theorem. We also establish an equivalence between a polynomial equation and a set of partial differential equations. We finally comment on a differential equation which arises after a small scale transformation and should concern all relations between metric quantities.
