#math

[vedalkensamurai]

z_(n+1) = sin(i^(1+4t) sinh(z_n)) + c if n is even

z+(n+1) = sinh(i^(1-4t) sin(z_n)) + c if n is odd

[sqrt-73]

Interesting math fact of the day #577:

For integer k > 0, p = 4k + 1 is prime iff

[terakuhn]

The first flight of the Martin Marietta X-24B lifting body rocket plane on 1973 August 1st was after the first flights of the Northrop M2-F3 lifting body rocket plane and the Apollo command and service module and was the last of the five US heavyweight lifting body designs flown between 1966 and 1975 to study vehicle designed for reentry from space. The Martin Marietta X-24B was a rebuild of the Martin Marietta X-24A.

Lifting bodies attempt to minimize drag by having a fuselage with little or no wing. This contrast flying wings which have a wing with little or no fuselage.

[vedalkensamurai]

z_(n+1) = f(t, n mod 10) sin(z_n) + c

where f is the function that outputs these points.

[395nm]

Imagine you have a collection of platonic and archimedian solids, all of which have side length 1.

The octahedron has exactly 4x the volume of the tetrahedron.

The cuboctahedron is 20x the tetrahedron

the truncated tetrahedron is 23x the tetrahedron

the truncated octahedron is 96x the tetrahedron

Are any of the other polyhedra integer multiples of the tetrahedron?

[iris-garciag]

[vedalkensamurai]

Elongated Square Cupola, or Diminished Rhombicuboctahedron

z_(n+1) = ½^a * (i^(16t) * (1 + cos(2πt))^a * z_n⁹ + i^(-4t) * (1 + cos(2π(t+⅓)))^a * z_n⁴ + i^(-8t) * (1 + cos(2π(t+⅔)))^a * z_n⁵) + c(-1)^n

a = log_((1+cos(π/3))/2)(½)