Re: 555 Timers
For T_high, you calculate it by making use of caps. (at pins 2 and 6) discharge equations,
And vise versa in case of T_low, where you calculate it from the charging equations of caps at pins 2,6..
I assume that you know how to write such charging and discharging equations,
then, knowing T_high and T_low, you can find easily the time constant of the circuit (time constant = RxC), by proper value of C you then can get R, and this will give square wave output with the required duration (duty cycle = 50%)...
If you need further information, then let me know,
Best Regards,
Ahmad,