A List of Triangular Numbers are 1, 3, 6, 10, 15, 21, ...
Can you find a pattern to find the number of dots for any term, say the 25th? (click here for a formula)
A famous theorem for quickly adding the first 100 counting numbers discovered by a 10 year old boy  Carl Friedrich Gauss  along with two proofs; one algebraic, the other geometric
(Presentation by Dr. Edward Burger, Williams College from his Great Course on Number Theory)
(Presentation by Dr. Edward Burger, Williams College from his Great Course on Number Theory)


Below is one more elegant little pattern coming out of explorations with summing consecutive Triangular Numbers together. This is an area of mathematics called Number Theory. One presentation uses a visual, geometric approach to proving the conjecture to be true for any such numbers, the second looks at the proof algebraically.
(Presentation by Dr. Edward Burger, Williams College from his Great Course on Number Theory.)
(Presentation by Dr. Edward Burger, Williams College from his Great Course on Number Theory.)

