Heron's Formula Calculator
Semiperimeter (s): -
Area: -
Understanding Heron's Formula
What is Heron's Formula?
Heron's formula (also known as Hero's formula) calculates the area of a triangle using only its side lengths.
Key Formulas
Area = √(s(s-a)(s-b)(s-c))
where s = (a + b + c)/2 (semiperimeter)
and a, b, c are the side lengths
Historical Context and Development
Ancient Origins
Discovered by Heron of Alexandria
First century AD mathematics
Greek geometric innovation
Mathematical Impact
Revolutionized triangle calculations
Influenced modern geometry
Basis for advanced formulas
Modern Applications
Surveying and mapping
Computer graphics
Engineering design
Related Concepts
Brahmagupta's formula
Trigonometric equivalents
Complex plane applications
Advanced Properties
Triangle Inequalities
a + b > c
b + c > a
c + a > b
Determines triangle existence
Special Cases
Right triangles
Equilateral triangles
Isosceles triangles
Degenerate triangles
Generalizations
3D extensions
Non-Euclidean versions
Complex plane variants
Higher dimensions
Numerical Analysis
Computational stability
Error analysis
Alternative formulations
Optimization methods