Teaching materials · Cycle 1
Olympiad Geometry & Number Theory.
The Academy's opening cycle. Four sessions in autumn 2025 built the geometric and number theoretic instincts that carry through every later cycle.
Coach: Melih Üçer. Four sessions, 14 September, 28 September, 12 October, 26 October 2025. Closed 9 November 2025 with a cohort teacher presentation.
What the cycle covered
- 14 September 2025. Angle chasing, classical, directed and oriented angles.
- 28 September 2025. Miquel's lemma and circle problems.
- 12 October 2025. Divisors, gcd and coprimality.
- 26 October 2025. Gcd identities and exponential Diophantine problems.
The cycle emphasised the working geometer's toolkit, directed and oriented angles, cyclic quadrilaterals, spiral similarity, and the corresponding habits in elementary number theory, closing with problems that live between the two subjects.
Problem sets
The exercises from Cycle I.
The full exercise collection worked across the opening cycle, kept as a single document so the mathematics can be revisited in its original form.
These are the exercises used in the cycle's sessions. Individual problems are drawn from the olympiad problem literature and compiled for the Academy's teaching.