00:00Our lunar exploration project was born in 1969.
00:04Of course, some obstacles have challenged our path,
00:07but the astronomers remain convinced that we will soon return to the Moon,
00:12better equipped in terms of knowledge and technology.
00:15However, an eight-century-old method could prove more precious
00:19than the most advanced GPS technologies or the most efficient rockets.
00:24It is designated under the name of Fibonacci Sphere.
00:27This concept, highlighted by researchers from a Hungarian university,
00:32could offer a new perspective on lunar rotation and the flattening of the Moon
00:36when it orbits around the Earth.
00:39Contrary to the popular image of perfectly spherical stars floating in space,
00:43our planet and its satellite look more like slightly deflated football balls,
00:49due to gravitational forces, their rotation and tides.
00:53The Earth's GPS systems are already adapted to these imperfect shapes,
00:57our planet being slightly flattened at the poles.
01:00In the same way, if we plan to design a map system for the Moon,
01:05we must take into account its specific configuration,
01:08known as the solenoid,
01:10the lunar equivalent of the Earth's geoid, according to scientists.
01:14Since the Moon is less compressed than our planet,
01:17researchers have long simplified their model by considering the satellite as a perfect sphere.
01:23However, with the advent of ambitious projects in the next decades
01:27and the possibility of human missions on the Moon,
01:29an increased precision is required.
01:31Scientists now insist on the importance of collecting precise data
01:36in order to produce a faithful representation of the Moon.
01:39This is where the Fibonacci Sphere comes into play.
01:42This method, used by mathematicians to uniformly distribute points on a sphere,
01:47has recently made it possible to map about 100,000 lunar zones
01:51based on data collected by NASA.
01:54The results obtained have been decisive in refining our understanding of the lunar shape.
02:00Thus, it has been established that the lunar poles
02:02were closer to the center than the equator by nearly half a kilometer.
02:06This detail, although subtle, could make a big difference.
02:10By adjusting the GPS software, consequently, before setting foot on the Moon,
02:14we could avoid many disadvantages.
02:16Such a level of calculation, unequal since the 1960s,
02:20strengthens the preparation of scientists
02:22to face the challenges of the next space missions,
02:25as they have already done so here on Earth.
02:28This is not the first time that Fibonacci discoveries
02:30have been used to design ingenious solutions.
02:34They have also found applications in fields such as finance,
02:38agriculture, and computer science.
02:41But where does all this come from?
02:43According to the legend, the Italian mathematician Fibonacci
02:46was not particularly interested in the mathematical sequence at the origin,
02:51but rather in the rabbit.
02:53This is how he imagined a fascinating riddle.
02:57He wondered what would happen if they placed a couple of rabbits
03:00in a given space for a year, while setting certain theoretical rules.
03:04First, each couple of rabbits is composed of a male and a female,
03:08and the latter cannot begin to reproduce after only one month.
03:12Every month, each couple gives birth to a new pair of rabbits.
03:15Finally, all rabbits are supposed to be immortal during this one-year period.
03:20By doing the calculations, Fibonacci obtained this series of numbers,
03:241, 1, 2, 3, 5, 8, 13, and so on.
03:29By observing this series,
03:30we notice that each number corresponds to the sum of the previous two.
03:34The first two represent the initial couple of rabbits.
03:38Then, the number 2 designates the first pair and their first offspring.
03:43This intriguing sequence quickly aroused the interest of mathematicians
03:47who began to analyze it in depth.
03:50They discovered that this pattern was frequently found in nature,
03:53whether in the arrangement of leaves on a plant
03:56or the arrangement of seeds on a sunflower.
03:59There is even a simple experiment that you can try to explore this concept.
04:03Take a piece of paper and a pen,
04:06then try to draw the Fibonacci spiral.
04:08Start with a tiny circle,
04:11then gradually widen it by following the numbers of the sequence.
04:15The first circle will correspond to a point, or to zero.
04:19The next will measure a unit, followed by another circle of the same size.
04:24Continue like this, and you will see a harmonious spiral appear
04:27that retains its shape, regardless of its enlargement.
04:31You may have already crossed the Fibonacci spiral used as a symbol of hypnosis.
04:36Although the scientific evidence on this subject is limited,
04:40its effects on concentration and optic nerves are undeniable.
04:44After fixing a rotating spiral,
04:47you could see that the objects seem to shrink or enlarge
04:51depending on the direction of the movement.
04:53This sensory experience explains why some people describe it as hypnotizing.
04:59This fascinating series of numbers finds its place in our daily life,
05:03sometimes without us being aware of it.
05:05It can also have practical uses, like the conversion of miles into kilometers.
05:10Let's take this series.
05:12Choose two consecutive numbers, for example 13 and 21.
05:16If you perform the calculations,
05:18you will see that 13 miles corresponds to about 21 kilometers.
05:22The same principle applies to 34 and 55.
05:26Music and mathematics seem, at first glance, to belong to different worlds.
05:31However, Mozart would probably have disputed this idea.
05:35This musical genius would have nourished, from the beginning of his career,
05:38a passion for numbers.
05:40He liked to unleash intriguing digital motifs in his compositions,
05:43as if he were concealing secret messages.
05:46His sister even remembered him
05:48scribbling calculations on the margins of his scores.
05:51Some researchers say that he experimented with the numbers of Fibonacci,
05:55potentially using their ratios to harmonize his works.
05:59And in other forms of art?
06:01It is said that Leonardo da Vinci integrated the number of gold
06:04into his emblematic creations,
06:05such as the Man of Vitruvius and the famous Joconde.
06:09This same motif is found, moreover,
06:11in architectural marvels such as the Parthenon,
06:14whose judiciously spaced columns testify to this influence.
06:18The Great Pyramid of Giza would be another striking example.
06:21Although no official evidence confirms this link,
06:24its structure is so close to the number of gold that it can only intrigue.
06:28This motif also manifests itself in the nature around us.
06:32Walk in a garden and observe pineapples.
06:35Their scales are organized according to a scheme similar to the Fibonacci spiral.
06:40Even the development of human bones follows these proportions.
06:42Our body illustrates this harmony.
06:44A torso, a head, a heart.
06:47Some bodily characteristics also recall this model.
06:51The elements in pairs, such as our arms, legs, eyes and ears,
06:55follow this logic.
06:56And for the number 3,
06:58think of the structure of our hands, divided into three sections.
07:01The wrist, the palm and the fingers,
07:04themselves segmented into three.
07:06Moreover, the length of the bones of our fingers also respects this ratio.
07:10This design facilitates their movement,
07:12especially when it comes to grasping objects.
07:15The rest of Fibonacci is found in the curvature of oceanic waves
07:19and the way in which rivers divide and flow.
07:22Meteorological phenomena are no exception.
07:25Some whirlwinds and hurricanes adopt a formation and a propagation
07:28that recall the Fibonacci spiral.
07:31By broadening our perspective,
07:33we discover that these spirals are not limited to Earth.
07:36They are omnipresent in the universe and this is not a coincidence.
07:40The majority of galaxies, including our Milky Way,
07:43take the form of a spiral.
07:45Here is why.
07:46In a young galaxy,
07:48stars generally do not appear all at once.
07:51Some form faster,
07:53while others take longer.
07:55This variation influences gravity,
07:58which acts differently depending on the zones
08:00and rotates the young galaxy like a disc.
08:02This movement, combined with differences in gravity,
08:05stretches the galaxy to create its spiral arms.
08:08Conversely, if all the stars appear at once,
08:11gravity tends to crush the galaxy,
08:14giving it an ovoid shape,
08:16a type of galaxy that astronomers call elliptic.
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