What makes a tall structure stable?

After having scrutinized many tall structures, I have discovered that the key factor in constructing a tall structure is the firmness of the base. A tall structure always has a very large, heavy, and strong base that will support the weight of the top parts of the structure. For instance, the tallest building in the world, Burj Khalifa in Dubai, has a very rigid, strong base that holds up 828m of height. Moreover, most tall skyscrapers are constructed in a way that the circumference or the perimeter of the building descend as the building rises. This structure of gradually descending in diameter or perimeter helps lessen the burden of the base because each part is built bigger that the upper part so that the below part can support the weight of the upper part. There are many types of structure with which many tall structures are designed. One of the common type is a hyperboloid structure. Hyperboloid structures are superior in stability towards outside forces than "straight" buildings, but have shapes often creating large amounts of unusable volume (low space efficiency) and therefore are more commonly used as a purpose driven structure, such as water towers (to support a large mass), cooling towers, and aesthetic features.

Burj Khalifa

World's First Hyperboloid Structure, 1896

Websites:
http://en.academic.ru/dic.nsf/enwiki/2022226
http://www.globalarchitectsguide.com/library/Hyperboloid-structure.php
http://science.howstuffworks.com/engineering/structural/skyscraper.htm
http://en.wikipedia.org/wiki/Skyscraper