solutions of T^3 ...:
r: 3.84149900754350784631, r/4: 0.960374751885876961578; 4R: 7.07411660987074006047, R: 1.76852915246768501512
solutions of T^20 ...:
r: 3.62655316169497372588, r/4: 0.906638290423743431469; 4R: 5.89878151120986279451, R: 1.47469537780246569863
r: 3.93751641898303065892, r/4: 0.984379104745757664730; 4R: 7.62900271179488812492, R: 1.90725067794872203123
r: 3.97776044093697244107, r/4: 0.994440110234243110268; 4R: 7.86705724360915253766, R: 1.96676431090228813441
r: 3.99758252390476252425, r/4: 0.999395630976190631063; 4R: 7.98550098761924619014, R: 1.99637524690481154754