graph of time constant rc network

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Bhuvanesh123

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in the below image u see that time constant is 0.37 of initial value and 63% of final value.if that so see the second graph in that image the point should be on 0.37 (from initial value) but actually the time constant point is on 0.63.
this is messing with my i dont know what i misunderstood.
 

The graph on the left side is the capacitor discharging into the resistor. It begins to discharge quickly because the voltage on the capacitor is the highest which makes the discharging current the highest.

The graph on the right side is a capacitor charging. It begins to charge quickly because the voltage across the resistor is the highest then the charging current in the resistor is the highest.
 

In one time constant the output reaches the (0.37*initial_value + 0.63*final_value).
In the left figure: initial_value=1, final_value=0
In the right figure: initial_value=0, final_value=1

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