I had seen in a YouTube video how the spherical bubbles, when clumped together, took the hexagonal shape as the most efficient way to occupy the space

Some time ago I saw how air bubbles stacked on top of a container with a liquid oil, and it was shown in what way, the bubbles, spherical in origin, when pressed between them transformed their shape into hexagons. Just as in the case of the honeycomb where the hexagonal shape shows how nature organizes the shape in the most efficient way possible. In the case of the foam that formed on the top of the glass that I used for the gallery of photos that are below, in my first observation I had the impression to see that the bubbles were spherical, when taking the photo I saw by enlarging the images that effectively adopted the hexagonal shape when they were imprisoned between them.

I wonder if a detergent pump knows mathematics?
.

Because it is a perfect sphere. Perhaps simply, we live in a universe in which systems tend to balance and naturally tend to optimize energy. The interesting thing about the great geometries, the bees, is the way in which they build the bottom of their hexagonal cells, using 3 sloping rhombuses in the most efficient way possible.

«Bees, by virtue of a certain geometric intuition, know that the hexagon is greater than the square and that the triangle, and that it can contain more honey with the same material expense.»

Pappus of Alexandria

“The bees build their combs as regular hexagonal prisms pointed at the bottom by three diamonds inclined with respect to the horizontal by a certain angle so that, storing the same amount of honey, they have the minimum amount of matter (wax); that is, the area is minimal. This problem of bees has already admired the classics and was studied by important mathematicians, among others Colin McLaurin (1698-1746) and Gabriel Cramer (1704-1752), obtaining values ​​of 70º 32´ and 70º 31´ respectively for this inclination. »
Pappus de Alejandría

«“The bees build their combs as regular hexagonal prisms pointed at the bottom by three diamonds inclined with respect to the horizontal by a certain angle so that, storing the same amount of honey, they have the minimum amount of matter (wax); that is, the area is minimal. This problem of bees has already admired the classics and was studied by important mathematicians, among others Colin McLaurin (1698-1746) and Gabriel Cramer (1704-1752), obtaining values ​​of 70º 32´ and 70º 31´ respectively for this inclination.»

Bees and mathematics.
José Carrión Beltran


Hexagonos: El codigo de la Naturaleza (Forma y… por raulespert

I had seen in a YouTube video how the spherical bubbles, when clumped together, took the hexagonal shape as the most efficient way to occupy the space

Some time ago I saw how air bubbles stacked on top of a container with a liquid oil, and it was shown in what way, the bubbles, spherical in origin, when pressed between them transformed their shape into hexagons. Just as in the case of the honeycomb where the hexagonal shape shows how nature organizes the shape in the most efficient way possible. In the case of the foam that formed on the top of the glass that I used for the gallery of photos that are below, in my first observation I had the impression to see that the bubbles were spherical, when taking the photo I saw by enlarging the images that effectively adopted the hexagonal shape when they were imprisoned between them.

I wonder if a detergent pump knows mathematics?

Because it is a perfect sphere. Perhaps simply, we live in a universe in which systems tend to balance and naturally tend to optimize energy. The interesting thing about the great geometries, the bees, is the way in which they build the bottom of their hexagonal cells, using 3 sloping rhombuses in the most efficient way possible.

«Bees, by virtue of a certain geometric intuition, know that the hexagon is greater than the square and that the triangle, and that it can contain more honey with the same material expense.»
Pappus of Alexandria

“The bees build their combs as regular hexagonal prisms pointed at the bottom by three diamonds inclined with respect to the horizontal by a certain angle so that, storing the same amount of honey, they have the minimum amount of matter (wax); that is, the area is minimal. This problem of bees has already admired the classics and was studied by important mathematicians, among others Colin McLaurin (1698-1746) and Gabriel Cramer (1704-1752), obtaining values ​​of 70º 32´ and 70º 31´ respectively for this inclination. »

Bees and mathematics.
José Carrión Beltran

Hexagons: The code of Nature (Form and … by raulespert

We will have to continue studying this manifestation in the various objects in nature.