论文标题
北极星：导航的数学和地球形状
Polaris: The Mathematics of Navigation and the Shape of the Earth
论文作者
论文摘要
对于千年而言，水手们使用了经验规则，即北极星的高度角度，北极星的高度角度，通过六分，象限或阿果曲布群测量，大约等于纬度。在这里，我们使用基本三角学表明，经验定律1可以从启发式转换为定理。第二个古老的经验定律是，从观察者到北极的距离是沿着行星球形表面测得的地球距离，是结实度的数量乘以111.1公里。经验法2是否可以同样严格地渲染？不;尽管地球的形状受到三角学的控制，但我们世界的规模是宇宙学历史的偶然事故。但是，经验法2可以通过测量进行严格验证。 111公里的南北距离与一个纬度的距离的关联在微不足道的纬度上产生了40,000公里的圆周。我们还将这些想法和平行射线近似扩展到建模平坦的三种方式。我们表明，由非常昂贵的卫星拍摄的轨道的照片是不需要使平坦地球难以置信的；简单的数学也证明了地球是一个领域。
For millenia, sailors have used the empirical rule that the elevation angle of Polaris, the North Star, as measured by sextant, quadrant or astrolabe, is approximately equal to latitude. Here, we show using elementary trigonometry that Empirical Law 1 can be converted from a heuristic to a theorem. A second ancient empirical law is that the distance in kilometers from the observer to the North Pole, the geodesic distance measured along the spherical surface of the planet, is the number of degrees of colatitude multiplied by 111.1 kilometers. Can Empirical Law 2 be similarly rendered rigorous? No; whereas as the shape of the planet is controlled by trigonometry, the size of our world is an accident of cosmological history. However, Empirical Law 2, can be rigorously verified by measurements. The association of 111 km of north-south distance to one degree of latitude trivially yields the circumference of the globe as 40,000 km. We also extend these ideas and the parallel ray approximation to three different ways of modeling a Flat Earth. We show that photographs from orbit, taken by a very expensive satellite, are unnecessary to render the Flat Earth untenable; simple mathematics proves Earth a sphere just as well.
