team 8 - counting triangles, 2018 chapter team 8; can use square counting first, then time 2??? not working; 385 not 315 not working

there's formula for this triangle counting, similar to sum of n^2: floor of n(n+2)(2n+1)/8

sum of n n(n+1)/2

sum of squares: n(n+1)(2n+1)/6

sum of cubes: n^2(n+1)^2/4

https://brilliant.org/wiki/sum-of-n-n2-or-n3/

https://www.youtube.com/watch?v=9EU3FlKj-3M counting triangles

partial work http://jwilson.coe.uga.edu/EMAT6680Fa06/Kitchings/cnkEMAT6600/inprogress/Triangle%20Counting/trianglecounting2.html

sandra did baby-counting on base length, subcasing - 55+54+51+46+39+30+20+12+6+2=315

https://iu.box.com/s/s8no3qypnmjkt0lysdirxplicjy2bx2x

should have taken picture of sandra's sprint round!!! forgot

todo - ask IU math help office

Math Learning Center

Swain East 340 10-5pm for algebra others non-calculus 5-7pm for calculus

https://math.indiana.edu/student-portal/undergraduate/academic-support/math-learning-center.html

Arithmetic mean > geometry mean > harmonic mean

harmonic mean in geometry explained:

https://www.cut-the-knot.org/triangle/HarmonicMean.shtml

euler totient phi function

https://www.cut-the-knot.org/blue/Euler.shtml

chinese remainder theorem 辗转相除法

https://www.cut-the-knot.org/blue/chinese.shtml

sum up purdue test

%honey creek t7 3/8 is answer; hexagon and triangle

\question Given regular hexagon ABCDEF, what is the probability that a

randomly chosen point inside the hexagon is inside $\triangle PQR$,

where P is the midpoint of $\overline{AB}$, Q is the midpoint of $\overline{CD}$,

and R is the midpoint of $\overline{EF}$? Express your answer as a common fraction.