Euler's sum : Software simulation for 1/1²+1/2²+1/3²+1/4²+ ⋯ = π² / 6
Hi, Very famous Euler's sum must be radian ! 1/1²+1/2²+1/3² + ... = 1/1 + 1/4 + 1/9 + . . . Equation (1) What if the start term ( 1 over 1 ) is interpreted as arc-length 1 over circle radius 1 in view of geometric ? So the angle value of 1 over 1 is 1 radian or 57.29 degree. The second, the third can be calculated as 0.25(=14.32 degree), 0.111(=6.35 degree). All degree can be summed up so we can show these accumulated sum as graphically. Another words, all sequential number turns around circle as we sum up to infinity. Why not ? If this is proved right, that would be unbelievable but could be true ! There is detail of this below. My simulation's result is like below. There are some notes for above picture. 1) There are red, cyan, yellow arc and green filled arcs in the graphics. As every term in Equation (1) continues to increase, the color change from red to green and then red again circulately. So, there are color sequ...