Cyrene and Alexandria · c. 276-c. 194 BCE
Eratosthenes
Eratosthenes was mathematician, geographer, and librarian. He estimated Earth’s circumference from shadow angles and created a sieve for identifying prime numbers.
Biographical and historical reference works document Eratosthenes’s role and the mathematical work summarized on this page.
3-5, 6-8, 9-12, College
The person and the work
Biography
Eratosthenes was mathematician, geographer, and librarian associated with Cyrene and Alexandria. He estimated Earth’s circumference from shadow angles and created a sieve for identifying prime numbers.
The circumference method combines a local measurement, a central angle, and proportional reasoning over a whole circle. Together, these contributions connect number sense, fractions, ratios, and percentages, geometry and measurement, and trigonometry to the working problems, tools, and questions of the period.
Mathematical contribution
What this hero added or preserved
Core mathematical work
He estimated Earth’s circumference from shadow angles and created a sieve for identifying prime numbers.
Method, teaching, or application
The circumference method combines a local measurement, a central angle, and proportional reasoning over a whole circle.
Why this matters
The larger lesson
Eratosthenes shows that mathematics grows through proof, calculation, observation, design, teaching, or careful records. The lasting lesson is that number sense, fractions, ratios, and percentages, geometry and measurement, and trigonometry can turn a difficult question into a method another person can inspect and reuse.
Place the work in time
Timeline
- c. 276
Life and working period
Eratosthenes worked as mathematician, geographer, and librarian in Cyrene and Alexandria.
- Legacy
Lasting mathematical connection
The circumference method combines a local measurement, a central angle, and proportional reasoning over a whole circle.
Key idea
Numbers reveal structure
Eratosthenes’s story shows that numbers are not only labels. They can be classified, compared, decomposed, and arranged to reveal patterns.
When 801 is divided by 4, the quotient is 200 with remainder 1. That remainder is structural information, not a mistake.
Try it yourself
Find the quotient and remainder
Divide 801 by 4. State the quotient and remainder.
- Estimate how many full groups fit.
- Multiply the divisor by the quotient.
- Subtract to find the remainder.
Show the answer
801 = 4 × 200 + 1, so the quotient is 200 and the remainder is 1.
Math at work
Navigators and pilots use the same habits
Navigators and pilots use number sense to plan, compare, test, or communicate decisions. Eratosthenes’s work provides a historical example of that connection.
Keep curiosity alive
A little-known fact
The circumference method combines a local measurement, a central angle, and proportional reasoning over a whole circle.
Eratosthenes matters because of only one famous formula or anecdote.
The documented record is broader: He estimated Earth’s circumference from shadow angles and created a sieve for identifying prime numbers.
Keep exploring
Connected learning paths
Related math terms
- Place value
- Prime number
- Number pattern
- Ratio
Practice these ideas
- AdditionPractice adding whole numbers, integers, and decimals.
- SubtractionPractice subtracting whole numbers, including results below zero.
- 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.