### Hydrostatic Solution Of Particular Trinominial Equations

A. Demanet devised an interesting method of solution of trinomial equations which depends on the use of communicating vessels of convenient forms.
To solve an equation of the third degree of the form:
x3 + x = c
where c is a constant, an inverted cone and a cylinder, joined together by means of a tube, are taken.
As shown below.

The radius r of the cone and its height h are in the ratio:
r/h = √3/√π
while the base of the cylinder is taken as 1 cm2

### The Plant That Is Able To Count Almost To Five

We already knew birds can count, but what about plants? Is this idea so surrealist? No, it isn’t because research says the carnivorous plant with a suggestive name, Venus Flytrap (also referred to ‘Dionaea muscipula’), snaps its jaws shut only when the tiny hairs on the surface of the trapping structure formed by two lobes have been stimulated twice within a 20-second window. An additional stimulation primes the trap for digestion. Five stimulations trigger the production of digestive enzymes – and more additional hairs’ stimulations mean more enzymes.

### Numbers In Nature

Diaethria phlogea, the “89’98 butterfly”, is a species of butterfly of the Nymphalidae family found in Colombia, South America. The markings on its wing resemble a painted number: an 89, a 98 or even an 88.
Are there any other animals with numbers painted on their body?

### Cube in a Cube or the Intersecting Tetrahedra

A polyhedron compound of two cubes is obtained by allowing two cubes to share opposite polyhedron vertices, and then rotating one a sixth of a turn about the axis that joins the two opposite vertices (see fig. 1 below).

As you can see from fig. 2, the two-cube compound is made up of 12 pyramidal modules. Each pyramidal module is composed of two right triangles with ratio 2:1 and one isosceles right triangle.

Print the PDF with the paper model (shown in fig. 3) to make your own compound of two cubes. Continue reading “Cube in a Cube or the Intersecting Tetrahedra”