### Quick Answer

**Geometry is essential for applied mathematics, and it is used in architecture and engineering fields.** Its development was crucial in the development of modern mathematics. It can also make abstract mathematical concepts more clear.

### Full Answer

Math is an abstract field, but it often must be used in physical objects. Geometry provides a means of applying mathematical ideas to construction, vehicles and virtually all objects. When studying how strong a building's support will be, architects must use geometric reasoning. Similarly, geometry allows airplane designers to measure how aerodynamic a particular design is.

Geometry was essential for developing modern mathematics. The ancient Greeks studied geometry extensively, and many modern algebra theorems and axioms have their roots in Greek geometry. The Greeks also used proofs with geometry, and their work allowed later Arabic mathematicians to develop algebra and algorithms. Algebra, and therefore all continuous mathematics, have strong ties to geometric concepts.

Understanding the natural world also requires an understanding of geometry. Fractals, which revolutionized mathematics in the 20th century, depend on simple geometric patterns that repeat themselves. The structure of trees, for example, can be described mathematically using fractal techniques. Fractal designs also have an influence on fields including art, cryptography, biology and artificial intelligence.