地球出现土地分解为两个相等的部分——地球科学堆栈交换江南电子竞技平台江南体育网页版 最近30从www.hoelymoley.com 2023 - 07 - 07 - t23:05:15z //www.hoelymoley.com/feeds/question/19603 https://creativecommons.org/licenses/by-sa/4.0/rdf //www.hoelymoley.com/q/19603 3 地球出现了土地分解为两个相等的部分 xenoid //www.hoelymoley.com/users/20310 2020 - 04 - 16 - t10:23:15z 2020 - 04 - 16 - t17:41:07z < p >是存在一种子午线正好有出现土地面积180°的东180°的西(假设它可能存在…)?如果没有子午线,还有其他大圆的财产吗?< / p > < p >编辑:因为大卫Hammen证明存在这样一个值,它是哪一个?< / p > < p >什么是尽可能多的土地上出现的纬度比其南北(一个必然存在)?< / p > < p >我发现这< a href = " https://en.wikipedia.org/wiki/Hemispheres_of_Earth " rel = " nofollow noreferrer " >维基百科文章< / >但并不回答了这个问题。< / p > //www.hoelymoley.com/questions/19603/-/19604 # 19604 2 回答大卫Hammen分裂地球的土地出现两个相等的部分 大卫Hammen //www.hoelymoley.com/users/239 2020 - 04 - 16 - t16:51:33z 2020 - 04 - 16 - t16:51:33z < p > TL;博士:这取决于如何定义土地面积。与一个合理的定义,这样的子午线(连同其完成地球的另一边)一定会存在由于中间值定理。也是一样的自由。< / p > <人力资源> < p > < / p > < ul >定义函数<李> < p > <跨类= " math-container " > \美元operatorname{一}_ {E}}{\文本(\λ)< / span >美元的面积是陆地的半球投射到参考椭球体的东部的经度<跨类= " math-container " > \λ< / span >美元。李李< / p > < / > < > < p > <跨类= " math-container " > \美元operatorname{一}_ {W}}{\文本(\λ)$ < / span >土地的面积是投射到参考椭球体的半球向西经度线类< span = " math-container " > \λ< / span >美元。李李< / p > < / > < > < p > <跨类= " math-container " > \美元operatorname{\δA} _{朗}}{\文本(\λ)$ < / span >的区别是< span class = " math-container " > $ \ operatorname{一}_ {E}}{\文本(\λ)$ < / span >和<跨类= " math-container " > $ \ operatorname{一}_ {W}}{\文本(\λ)$ < / span >。李李< / p > < / > < > < p > <跨类= " math-container " > \美元operatorname{一}_ {N}}{\文本(\φ)$ < / span >土地的面积是投射到参考椭球体半球向北的纬度线类< span = " math-container " > \φ< / span >美元。李李< / p > < / > < > < p > <跨类= " math-container " > \美元operatorname{一}_{年代}}{\文本(\φ)$ < / span >土地的面积是投射到参考椭球体的半球向西经度线类< span = " math-container " > \φ< / span >美元。李李< / p > < / > < > < p > <跨类= " math-container " > \美元operatorname{\δA} _ {lat}}{\文本(\φ)$ < / span >的区别是< span class = " math-container " > $ \ operatorname{一}_ {N}}{\文本(\φ)$ < / span >和<跨类= " math-container " > $ \ operatorname{一}_{年代}}{\文本(\φ)$ < / span >。< / p > < /李> < / ul > < p >我的定义让每一个连续函数。注意:其他土地面积可能导致非连续函数的定义。想象一个完全垂直的悬崖,从北到南。如果这个悬崖的面积计算土地面积那么<跨类= " math-container " > \美元operatorname{\δA} _{\文本{朗}}(\λ)< / span >美元不会是连续的。这同样适用于< span class = " math-container " > $ \ operatorname{\δA} _{\文本{lat}}(\φ)< / span >美元完全垂直的悬崖,东到西。< / p > < p >证明纬度线必须存在是很容易的,所以我先这样做。 All of the Earth's land area is north of 90° south latitude, making $\operatorname{\Delta A}_{\text{lat}}(-90)$ a large positive number. All of the Earth's land area is south of 90° north latitude, making $\operatorname{\Delta A}_{\text{lat}}(90)$ a large negative number. Because zero is between this large negative number and large positive number, and because $\operatorname{\Delta A}_{\text{lat}}(\phi)$ is continuous, there must necessarily exist at least one line of latitude $\phi$ for which $\operatorname{\Delta A}_{\text{lat}}(\phi)$ is zero.

Regarding longitude, Pick an arbitrary longitude $\lambda$. If $\operatorname{\Delta A}_{\text{lon}}(\lambda)$ is zero we have a winner. If it's not zero, then since $\operatorname{\Delta A}_{\text{lon}}(\lambda +180°) = -\operatorname{\Delta A}_{\text{lon}}(\lambda)$, there exists at least one longitude $\lambda_0$ between $\lambda$ and $\lambda+180°$ where $\operatorname{\Delta A}_{\text{lon}}(\lambda_0)$ is zero.

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