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*The Bernoulli Family*

The Bernoullis were truly a prolific scientific family, in three generations this remarkable Swiss family produced eight mathematicians – three of them outstanding – who in turn had a swarm of descendants who distinguished themselves in many fields.

Jakob Bernoulli (1654-1705) studied theology at the insistence of his father, but abandoned it as soon as possible for science. He taught himself the calculus and became professor of mathematics at Basel. He wrote on infinite series, studied many special curves, invented polar coordinates and introduced the Bernoulli numbers that appear in the power series expansion of the tangent function. In his book *Ars Conjectandi* he formulated the basic principle in the theory of probability known as *Bernoulli’s theorem: i*f the probability of a certain event is *p*, and we run *n* independent trials out of which we get *k* successes, then the ratio of the successes to the trials *k/n* tends to the probability *p* as the number of trials n tends to infinity.

Jakob’s younger brother Johann Bernoulli also made a false start in his career, by studying medicine but he also became fascinated by calculus and applied it to many problems in geometry, differential equations, and mechanics. In 1695 he was appointed professor of mathematics and physics at Groningen in the Netherlands, and on Jakob’s death he succeeded his brother in the professorship in Basel.

The Bernoulli brothers sometimes worked on the same problems, which was unfortunate in view of their jealous and touchy dispositions. On occasion the friction between them flared up into a bitter and abusive fight, as it did over the brachistochrone problem. In 1696 Johann proposed the problem as a challenge to the mathematicians of Europe. It aroused great interest , and was solved by Newton and Leibnitz as well as by the two Bernoullis. Johann’s solution turned out to be more elegant, while Jakob’s one although rather clumsy and labourious was more general.

Johann’s son was Daniel Bernoulli (1700-1782), who also studied medicine like his father and who also gave way to his talent and became a professor of mathematics at St Petersburg. In 1733 he returned to Basel and was successively professor of botany, anatomy and physics. In his famous book *Hydrodynamica* he discussed fluid mechanics and gave the earliest treatment of he kinetic theory of gases. He is considered by many to have been the first genuine mathematical physicist.

**NEWS**

*Hayabusa*

On June 13th 2020 the Japanese unmanned spacecraft Hayabusa landed over southern Australia. Hayabusa or Falcon in Japanese, was launched on May 2003 to visit the near-Earth asteroid Itokawa. Hayabusa was meant to take a sample from the asteroid and bring it home. However, it seems that the capture mechanism malfunctioned and scientists expect that some material might have found its way inside the probe.

*Prehistoric Hair*

Palaeontologists from the University of Rennes, France have discovered two mammal hairs encapsulated in a piece of amber 100 million years old. Analysis of the hairs revealed that they have similar structure to fur of modern mammals but the identity of the animal is not known.

*Entangled Photon Source*

A group of researchers from Toshiba Research Europe and the University of Cambridge produced a new way to generate entangled photons, a key ingredient for quantum computing. The electonicdevice, called an entangled light-emitting diode is produced in a similar way to existing LEDs in combination with a quantum dot.

*Radiation Law in San Francisco*

San Francisco will become the first city in the United States to require all mobile phone retailers to quote radiation levels in the handsets they sell. Although some studies have suggested that mobile phone radiation is not harmful to people, the bill defines an amount of radio waves that people can safely absorb when using the devices.

*Flower power*

According to researchers from the University of Chicago, the world is a cooler, wetter place because of flowering plants. The researchers carried out simulations that demonstrate the importance of flowering-plant physiology in climate regulation in the ever-wet forest. Flowering plants are highly efficient at transpiring water from the soil back into their surroundings. This recycling process depends on transpiration and it would have been much slower in the absence of flowering plants.