Khwarazm, Central and South Asia · 973-c. 1050
Al-Biruni
Al-Biruni was mathematician, astronomer, geographer, and scholar. He used trigonometry and careful measurement to determine coordinates, distances, and an estimate of Earth’s radius.
Biographical and historical reference works document Al-Biruni’s role and the mathematical work summarized on this page.
3-5, 6-8, 9-12, College
The person and the work
Biography
Al-Biruni was mathematician, astronomer, geographer, and scholar associated with Khwarazm, Central and South Asia. He used trigonometry and careful measurement to determine coordinates, distances, and an estimate of Earth’s radius.
His mountain-horizon method estimates Earth’s size from a measured height and dip angle. Together, these contributions connect fractions, ratios, and percentages, geometry and measurement, trigonometry, and statistics and probability to the working problems, tools, and questions of the period.
Mathematical contribution
What this hero added or preserved
Core mathematical work
He used trigonometry and careful measurement to determine coordinates, distances, and an estimate of Earth’s radius.
Method, teaching, or application
His mountain-horizon method estimates Earth’s size from a measured height and dip angle.
Why this matters
The larger lesson
Al-Biruni shows that mathematics grows through proof, calculation, observation, design, teaching, or careful records. The lasting lesson is that fractions, ratios, and percentages, geometry and measurement, trigonometry, and statistics and probability can turn a difficult question into a method another person can inspect and reuse.
Place the work in time
Timeline
- 973
Life and working period
Al-Biruni worked as mathematician, astronomer, geographer, and scholar in Khwarazm, Central and South Asia.
- Legacy
Lasting mathematical connection
His mountain-horizon method estimates Earth’s size from a measured height and dip angle.
Key idea
Proportion preserves a relationship
Al-Biruni’s work connects quantities by ratio. Scaling both parts by the same factor keeps the relationship unchanged.
The ratio 6:9 scaled by 2 becomes 12:18.
Try it yourself
Scale a ratio
Scale the ratio 6:9 by a factor of 2.
- Multiply the first term by the scale factor.
- Multiply the second term by the same factor.
- Confirm that both ratios simplify to the same value.
Show the answer
The scaled ratio is 12:18.
Math at work
Navigators and pilots use the same habits
Navigators and pilots use fractions, ratios, and percentages to plan, compare, test, or communicate decisions. Al-Biruni’s work provides a historical example of that connection.
Keep curiosity alive
A little-known fact
His mountain-horizon method estimates Earth’s size from a measured height and dip angle.
Al-Biruni matters because of only one famous formula or anecdote.
The documented record is broader: He used trigonometry and careful measurement to determine coordinates, distances, and an estimate of Earth’s radius.
Keep exploring
Connected learning paths
Related math terms
- Ratio
- Proportion
- Percentage
- Angle
Practice these ideas
- Fractions & DecimalsWork with fractions, decimals, percentages, and conversions.
- Pre-AlgebraBridge arithmetic and algebra with integers, ratios, and equations.
- GeometryExplore shapes, angles, area, perimeter, volume, and classification.
- Advanced GeometryPractice coordinate geometry, transformations, vectors, and solids.
- TrigonometryUse angles, right triangles, radians, and trigonometric functions.