Triangular numbers - Roots with bases other than 1

AI Thread Summary
Calculating the square root of triangular numbers with bases other than 1 can be approached by dividing the triangular number by the base. For example, using base 2, triangular numbers like 2, 6, 12, and 20 can be simplified. The user initially sought assistance but later figured out the method independently. This approach allows for the application of the standard square root formula. Understanding this process can aid in working with various bases for triangular numbers.
Narf the Mouse
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Not sure where this should go, but - How would you calculate the square root of a triangular number with a base other than 1? For example, 2, 6, 12, 20 (Base 2).

Would rather have help to figure it out than the actual formula.
 
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Never mind - Realized I can just divide the number by the base and use the normal formula.
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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