l

Diophantine equation

Set of Solutions

$\delta =\frac{\pi }{2l}$

$\alpha =\frac{\pi }{l}$

$\beta =\left(1-\frac{1}{l}\right)\pi$

1

$t+s=4$

$\left\{\left(4,0\right),\left(0,4\right),\left(1,3\right),\left(3,1\right),\left(2,2\right)\right\}$ ¹

π/4

π/2

π/2

2

$t+2s=6$

$\left\{\left(6,0\right),\left(0,3\right),\left(4,1\right),\left(2,2\right)\right\}$

π/6

π/3

2π/3

3

$t+3s=8$

$\left\{\left(8,0\right),\left(5,1\right),\left(2,2\right)\right\}$

π/8

π/4

3π/4

4

$t+4s=10$

$\left\{\left(10,0\right),\left(6,1\right),\left(2,2\right)\right\}$

π/10

π/5

4π/5

5

$t+5s=12$

$\left\{\left(12,0\right),\left(7,1\right),\left(2,2\right)\right\}$

π/12

π/6

5π/6

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k

$t+\left(k-1\right)\cdot s=2k$

$\left\{\left(2k,0\right),\left(k+1,1\right),\left(2,2\right)\right\}$

π/2k

π/k

$\left(1-\frac{1}{k}\right)\pi$