discovered in 98 C.E

1. discovered in 98 C.E Kevin Call Matt Ragusa Austen Rerick Hanna Utkin PD8

2. On Menelaus Menelaus was a mathematician who lived during the Roman Empire in both Alexandria and Rome. His work was largely on the geometry of spheres. This theorem was first discussed in his book, Sphaerica, and later mentioned by Ptolemy in his work Almagest. It achieved wider familiarity when the 17th century Italian mathematician Giovanni Ceva expanded upon it in his theorem on the same subject. Menelaus’ Theorem proves that spheres are made up of spherical triangles. example of a spherical triangle example of a geodesic

3. Basic Concepts of the Menelaus Theory Given a triangle ABC, and a transversal line that crosses BC, AC and AB at points D,E and F respectively, with D,E and F distinct from A,B and C .

4. Menelaus Theory Example Problem B 4 M 8 E 12 6 A N 18 C 6 Remember: AM/MB × BE/EC × CN/NA

5. Solution: Step-by-Step AM/MB × BE/EC × CN/NA (12/4) × (8/6) × (6/24) = ? B 4 M 8 12 E 6 A C N 18 6

6. Logic Behind the Formula

7. Logic Behind the Formula

8. Real Life Applications • Celestial Navigation • Air Navigation • Architecture • Astronomy and Physics (‘Precession of the Equinoxes’)