Uploaded October 2025 | Updated September 2026, 1 week ago
Part 3 of 3:
This is the sequel to the classic "count the dots" problem, and this time, there's a trap. In a regular octagon, the beautiful symmetry hides a secret: multiple diagonals intersect at the same point. This cool animation breaks down the hidden math, untangles the overlaps, and reveals the true number of dots.
Part 1 of 3: Diagonals Counting Trick: youtu.be/QD5Q-vmQXQM
Part 2 of 3: Dot counting in odd-sided polygons: youtu.be/JcMI-BdMt68
Part 3 of 3: Dot counting in even-sided polygons: youtu.be/kw-fcOomE-Q
For more details, check out this research paper:
THE NUMBER OF INTERSECTION POINTS MADE BY THE DIAGONALS OF A REGULAR POLYGON
https://math.mit.edu/~poonen/papers/ngon.pdf
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Mastering AMC 10/12 book: omegalearn.org/mastering-amc1012.
The book includes video lectures for every topic on the AMC 10/12 contests, along with many useful formulas and hundreds of examples and practice problems with detailed video solutions.
Mastering AMC 8 book: omegalearn.org/mastering-amc8
The book covers the most important concepts on the AMC 8 contest, and includes video lectures for every chapter, formulas for every topic, and hundreds of examples and practice problems with detailed video solutions.
Join our Discord server to discuss problems from our books or any help with math competitions in general: bit.ly/OmegaLearnDiscord
-------------------------------------------------------------------------------------------------------------------------------------
To get notifications for new videos, click here to subscribe:
bit.ly/2JjEDqr
For more practice, watch the following free courses:
1. AMC 8 Fundamentals Course:
youtube.com/playlist?list=PLT9bNzqjDoMmMNsMAJ3g7C4ptRnPMMrpT
2. AMC 8 Advanced Course:
youtube.com/playlist?list=PLT9bNzqjDoMmjM-PFJktrlab4-bkWwFMP
3. Mastering AMC 8 Course:
youtube.com/playlist?list=PLT9bNzqjDoMnF2rmrySRQF_c_gUjKkVMe
4. AMC 10/12 Fundamentals Course:
youtube.com/playlist?list=PLT9bNzqjDoMkoIg9K_bs4EjdpHYlS0L51
5. Mastering AMC 10/12 Course:
youtube.com/playlist?list=PLT9bNzqjDoMlmyxKw2bp5nHsEu-Zn9dac
More resources available at: omegalearn.org
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Tags:
AMC 8, AMC 8 Preparation, AMC 8 Crash Course, AMC 8 Concepts, AMC 8 Review, AMC 10, AMC 12, MATHCOUNTS, MathLeague, Number Theory, Primes, Factors, Competition math, Number of Factors, Sum of Factors, Product of Factors, Permutations, Combinations, Combinatorics, Modular Arithmetic, Recursion, Probability, Divisibility, Competition Math, Area of a Triangle, Similar Triangles, Cyclic Quadrilateral, Power of a Point, 3D Geo, Polygons, Coordinate Geometry
Part 3 of 3:
This is the sequel to the classic "count the dots" problem, and this time, there's a trap. In a regular octagon, the beautiful symmetry hides a secret: multiple diagonals intersect at the same point. This cool animation breaks down the hidden math, untangles the overlaps, and reveals the true number of dots.
Part 1 of 3: Diagonals Counting Trick: youtu.be/QD5Q-vmQXQM
Part 2 of 3: Dot counting in odd-sided polygons: youtu.be/JcMI-BdMt68
Part 3 of 3: Dot counting in even-sided polygons: youtu.be/kw-fcOomE-Q
For more details, check out this research paper:
THE NUMBER OF INTERSECTION POINTS MADE BY THE DIAGONALS OF A REGULAR POLYGON
https://math.mit.edu/~poonen/papers/ngon.pdf
-------------------------------------------------------------------------------------------------------------------------------------
Mastering AMC 10/12 book: omegalearn.org/mastering-amc1012.
The book includes video lectures for every topic on the AMC 10/12 contests, along with many useful formulas and hundreds of examples and practice problems with detailed video solutions.
Mastering AMC 8 book: omegalearn.org/mastering-amc8
The book covers the most important concepts on the AMC 8 contest, and includes video lectures for every chapter, formulas for every topic, and hundreds of examples and practice problems with detailed video solutions.
Join our Discord server to discuss problems from our books or any help with math competitions in general: bit.ly/OmegaLearnDiscord
-------------------------------------------------------------------------------------------------------------------------------------
To get notifications for new videos, click here to subscribe:
bit.ly/2JjEDqr
For more practice, watch the following free courses:
1. AMC 8 Fundamentals Course:
youtube.com/playlist?list=PLT9bNzqjDoMmMNsMAJ3g7C4ptRnPMMrpT
2. AMC 8 Advanced Course:
youtube.com/playlist?list=PLT9bNzqjDoMmjM-PFJktrlab4-bkWwFMP
3. Mastering AMC 8 Course:
youtube.com/playlist?list=PLT9bNzqjDoMnF2rmrySRQF_c_gUjKkVMe
4. AMC 10/12 Fundamentals Course:
youtube.com/playlist?list=PLT9bNzqjDoMkoIg9K_bs4EjdpHYlS0L51
5. Mastering AMC 10/12 Course:
youtube.com/playlist?list=PLT9bNzqjDoMlmyxKw2bp5nHsEu-Zn9dac
More resources available at: omegalearn.org
-------------------------------------------------------------------------------------------------------------------------------------
Tags:
AMC 8, AMC 8 Preparation, AMC 8 Crash Course, AMC 8 Concepts, AMC 8 Review, AMC 10, AMC 12, MATHCOUNTS, MathLeague, Number Theory, Primes, Factors, Competition math, Number of Factors, Sum of Factors, Product of Factors, Permutations, Combinations, Combinatorics, Modular Arithmetic, Recursion, Probability, Divisibility, Competition Math, Area of a Triangle, Similar Triangles, Cyclic Quadrilateral, Power of a Point, 3D Geo, Polygons, Coordinate Geometry
