sentence1: What 's an intuitive explanation of the following mathematical fact : -LSB- math -RSB- \ displaystyle \ sum _ -LCB- n = 1 -RCB- ^ -LCB- \ infty -RCB- -LCB- \ frac -LCB- 1 -RCB- -LCB- n ^ 2 -RCB- -RCB- = \ frac -LCB- \ pi ^ 2 -RCB- -LCB- 6 -RCB- -LSB- / math -RSB- ?
sentence2: How do I intuitively understand -LSB- math -RSB- \ int _ -LCB- 0 -RCB- ^ -LCB- \ infty -RCB- e ^ -LCB- - x ^ 2 -RCB- dx = \ Gamma -LRB- \ frac -LCB- 3 -RCB- -LCB- 2 -RCB- -RRB- = \ frac -LCB- 1 -RCB- -LCB- 2 -RCB- ! = \ frac -LCB- \ sqrt -LCB- \ pi -RCB- -RCB- -LCB- 2 -RCB- -LSB- / math -RSB- ?