$\textsf{\LARGE S}$

Regular triangle?

The sum of the angles in any T-triangle is 4 T-radians. 
The T-triangle on the left is equilateral, but it is not equiangular.
The one on the right is equiangular, but it is not equilateral.
Actually, there are no regular T-triangles.

$\textsf{\LARGE 1}$

$\textsf{\LARGE 1}$

$\textsf{\LARGE 1}$

T-squares

Any E-square is also a T-square. 
But because the taxicab distance is not uniform in every direction, 
these two T-squares have the same perimeter (though not the same area).

The square on the left is also a T-circle. The one on the right is not.

T-radian

T-rotation

T-trigonometry

2

1

1

In the unit T-circle, we can define the T-radian exactly the same way we define an E-radian 
in the unit E-circle. To T-measure an angle, it's sufficient to measure the T-length 
of the corresponding (straight) arc on the unit T-circle. A T-circle has 8 T-radians.

$\textsf{\LARGE S'}$

1

The perpendicularity and parallelism are preserved under rotations, but, in general, 
T-distances are not invariant under either E-rotations or T-rotations. 
Here we see point S rotating 1 T-radian with respect to the origin of coordinates.

Trigonometric T-functions are much simpler than their Euclidean counterparts. 
For example, the T-sine function is not only non-transcendent but also piecewise linear. 
The T-tangent function is composed by piecewise E-hyperbolas.

4/3

4/3

4/3

1

4/3

1

B: (1, 0)
A: (-1, 0)
AB: abs(x(B) - x(A)) + abs(y(B) - y(A))
polígono2 = Polygon(B - (AB, 0), B - (0, AB), 4)
polígono1 = Polygon(A - (AB, 0), A - (0, AB), 4)
C, D = Intersect(polígono1, polígono2)
c1, m, t, d, e = Polygon(B, D, A, C)
S = Point(c1)
prS = PathParameter(S)
lado: 2.75
N = (-3.25, 1.5)
J = (11, 2.25)
I = (7.5, 2.25)
IJ: abs(x(I) - x(J)) + abs(y(I) - y(J))
j = Segment(I + ((-IJ), IJ) / 2, I + (0, IJ))
op3 = false
t1, c_1, a, b = Polygon(B, A, D)
γ, δ, ε = InteriorAngles(t1)
op4 = false
E: (1.5, -1)
F: E + (AB, 0)
polígono3, f, g, h, i, G, H = Polygon(E, F, 4)
O: N + (lado, 0)
NO: abs(N - O)
polígono5 = Polygon(N - (NO, 0), N - (0, NO), 4)
l = Segment(N - (NO, 0), N + (0, NO))
n = Ray(N, Rotate[O, 120°, N])
P = Intersect(l, n)
polígono8 = Polygon(P - (NO, 0), P - (0, NO), 4)
p = Ray(P, Rotate[N, 120°, P])
q = Segment(P + (NO, 0), P + (0, NO))
Q = Intersect(p, q)
r = LineBisector(N, O)
Q' = Mirror(Q, r)
P' = Mirror(P, r)
R = (3.5, 1.5)
W = (4.25, -0.5)
Z: W + (2.25, 0)
A_1: W + (7, 0)
WZ: abs(W - Z)
Z' = Rotate(Z, 22.5°, W)
B_1: A_1 + Z' - W
O_1: W - (8, 0)
P_1: O_1 + (WZ, 0)
q_2 = Ray(O_1, Rotate[P_1, 135°, O_1])
r_2 = Segment(O_1 - (WZ, 0), O_1 + (0, WZ))
Q_1 = Intersect(q_2, r_2)
s_2 = Ray(Q_1, Rotate[O_1, 135°, Q_1])
t_2 = Segment(Q_1 - (WZ, 0), Q_1 + (0, WZ))
R_1 = Intersect(s_2, t_2)
a_2 = Ray(R_1, Rotate[Q_1, 135°, R_1])
b_2 = Segment(R_1 + (WZ, 0), R_1 + (0, WZ))
S_1 = Intersect(a_2, b_2)
c_2 = LineBisector(O_1, P_1)
T_1 = Mirror(S_1, c_2)
U_1 = Mirror(R_1, c_2)
V_1 = Mirror(Q_1, c_2)
op1 = true
op2 = false
op5 = false
S' = Point(c1, prS + 1 / 8 - floor(prS + 1 / 8))
α = Angle(S, (0, 0), S')
s(x) = 1 - (2 * abs(1 / 2 - x / 4 + (2 * floor(1 / 4 + x / 8))))
factor = 1
T = If(x(S) > 0 ∧ x(S') < 0, D, If[y(S) > 0 ∧ y(S') < 0, A, If[x(S) < 0 ∧ x(S') > 0, C, If[y(S) < 0 ∧ y(S') > 0, B, (S + S') / 2]]])
l1: {Polygon[(0, 0), S, T, S']}
c(x) = s(x + 2)
tt(x) = s(x) / c(x)
K: (1.5, 0)
L: K + (5, 1) / 6
V: K + (1, 5) / 6
l2: {Polygon[K, L, V]}
β = Angle(L, K, V)
ζ = Angle(V, L, K)
η = Angle(K, V, L)
k: abs(x(K - L)) + abs(y(K - L))
f_1 = Segment(K, L)
g_1 = Segment(L, V)
h_1 = Segment(V, K)
o: abs(x(V - L)) + abs(y(V - L))
u: abs(x(V - K)) + abs(y(V - K))
i_1 = Segment(S, S')

Tool: OpSuma
Elige O y luego dos puntos
Input: O, A, B
Output: O'

C = Midpoint(A, B)
O' = Mirror(O, C)

Tool: OpResta
Elige O, el primer punto y el segundo punto
Input: O, A, B
Output: O'

B' = Mirror(B, O)
C = Midpoint(A, B')
O' = Mirror(O, C)

Tool: OpProducto
Elige O e I, y luego dos puntos
Input: O, I, A, B
Output: E

I' = Mirror(I, O)
B' = Mirror(B, O)
c = Semicircle(I', I)
d = Semicircle(B', B)
f = Line(O, I)
g = OrthogonalLine(O, f)
C = Intersect(c, g, 1)
h = Line(C, A)
D = Intersect(d, g, 1)
i = Line(D, h)
E = Intersect(f, i)

Tool: OpDivisión
Elige O e I, y luego el primer punto y el segundo punto
Input: O, I, A, B
Output: E

f = Line(O, I)
g = OrthogonalLine(O, f)
I' = Mirror(I, O)
c = Semicircle(I', I)
Binv = Mirror(B, c)
Binv' = Mirror(Binv, O)
e = Semicircle(Binv', Binv)
F = Intersect(e, g, 1)
C = Intersect(c, g, 1)
h = Line(C, A)
i = Line(F, h)
E = Intersect(f, i)