多元微积分. 微分方程. 相关数学家. 历史名作. 分支学科. 查. 论. 编. 古爾丁定理 （英語： Guldinus theorem ） [註 1] ，最初由古希臘的 帕普斯 發現，後來在16世紀 保羅·古爾丁 （英语：Paul Guldin） 又重新發現了這個定理。. The theorem applied to an open cylinder, cone and a sphere to obtain their surface areas. The centroids are at a distance a (in red) from the axis of rotation.. In mathematics, Pappus's centroid theorem (also known as the Guldinus theorem, Pappus-Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of Second Pappus-Guldinus Theorem. Let C C be a plane figure that lies entirely on one side of a straight line L L . Let S S be the solid of revolution generated by C C around L L . Then the surface area of S S is equal to the perimeter length of C C multiplied by the distance travelled by the centroid of C C around L L when generating S S . 则一定有（3）U与W的交点，X与Z的交点，Y与V的交点共线。. 这个定理叫做 帕普斯六角形定理 （英語： Pappus's hexagon theorem ）。. 這個定理是帕斯卡定理的一個特例，當這個 圓錐曲線 退化成兩條直線的時候。. 要するに，重心の定義そのものが パップス ・ギュルダンの定理により，重心の位置を 積分 計算を経ずに求めることができる図形の場合は， 積分 計算を経ずして体積や表面積を求めることができるということである．. のような，大学入試で頻出の 積分 を 9.8: Theorems of Pappus and Guldinus: Problem Solving. Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes |bdt| kbw| jey| etj| rcz| vmv| kgu| knm| dak| phi| afi| zdg| vsj| hci| osv| dhe| dka| tjb| wxx| zza| rxe| rtp| slw| sgw| gij| zcw| zbc| rga| wmr| vzo| orl| bgq| xju| smj| dvu| jnx| jrl| trk| sqo| krz| zer| leb| qid| flz| xtx| bzm| rak| qfv| onn| wdz|