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Popular Science Magazine for Students and Their Parents
#62018
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ISSN 2537-7744 ISSN 2537-7744
JUNE 2018
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MATHEMATICS
TECHNOLOGY
Logic versus Intuition
Space Trash: how great a threat is it?
p. 4
p. 52
The history of
Dwellings p. 60
What is an
Irrational Number? p. 8
CHEMISTRY
The Polymer
Century p. 16
BIOLOGY
Why do we need
Cell Cultures? p. 30
How does a cell become an organism? p. 36
MEDICINE
How do Allergies develop?
p. 44
ECOLOGY
How can we Preserve Biomaterials? p. 66 The history of
Concrete
p. 90
ECONOMICS
What is a Budget? p. 72
MEGAPROJECT
What does the NASA’s Mars rover consist of ? p. 50
SKEPTIC
What is hidden from us? p. 80
SOCIETY
The most Exciting Bets in history p. 84
11
#15 J UNE 2018
Geometric Proof m Let √2 = n , where m and n are the smallest numbers possible that do not have any common divisors. Then 2n² = m², that is, the area of the square with side length m is equal to the sum of the areas of two squares with sides n. If the smaller squares are placed in opposite corners of the large square, their intersection will give us a new square with side m − 2(m − n) = 2n − m. The uncovered areas of the square are also squares with side m − n. From the equality of the area of the square with the side m and the sum of the squares with the side n we get that the area of the section of the plane where the squares 2n − m overlap is equal to the area of the uncovered sections inside the square, that is, (2n − m)² = 2(m − n)². It follows that √2 = m −n That is, the number √2 can be represented as a ratio of integers less than m and n, which were the smallest numbers possible! Hence, we have found a contradiction.
m n
n
(m–n)2 (2m–n)2
=
+
(m–n)2
Algebraic Proof If the number √2 can be expressed as a fraction, then we can write it as a ratio of the natural numbers a and b, b a , when a and b do not have common b factors (which means that the fraction is irreducible). namely √2 =
We multiply the equality by b and raise both sides of the square. We obtain 2b² = a².. Since the left-hand side of the equation is even, then a² must be divisible by 2,, and this is possible only for an even a. If a is even, we can represent it in the form a = 2с. But then, 2b² = 4 с²,, from which it follows that b²= b² = 2с², and this entails the parity of the number b.. So, we have obtained that a and b are are even numbers, but this contraa dicts the statement that the fraction b is irreducible. This contradiction proves the impossibility of representing √2 as a fraction.
CH E M IS T RY
THE POLYMERIC AGE
What are the threats to the environment?
P
eople have used polymers since the Stone Age wool and leather contain proteins cellulose is the main component of fabrics, papyrus and paper. Throwing out such materials would not make one concerned for the environment because they decompose fast. At the beginning of the 0th century, mankind mastered the manufacturing of artificial and synthetic polymers. The products proved to be light and durable, but… The coming of the polymeric age was overshadowed by the failure of nature to expediently get rid of such compounds. As a result, “man-made” polymers get piled up in giant quantities in landfills, and scientists are looking for ways to save the Earth from pernicious plastic.
Chain Molecules olymers, despite their low specific gravity, have a large molecular weight. Certain elements in these compounds — cross-links — are repeated periodically. In fact, polymers are old as life itself. The essential components of living systems are such polymers as proteins, nucleic acids and polysaccharides. These polymers are called natural. Those created by man — artificial and synthetic.
CHEMISTRY
There is a possibility that some organisms that evolutionally adapted to extracting microelements from synthetic polymers will come about. The list of bacteria is growing. In 0 , a bacterium processing polyethylene terephthalate (Ideonella sakaiensis) was discovered, and in 0 the list of creatures with unusual food habits was supplemented with a highly organi ed organism — the wax moth larva Galleria mellonella). It digests polyethylene, splitting it to ethylene glycol. n the one hand, it’s good that there are ways of biological processing of plastic. n the other, they are fraught with danger such organisms may eventually feed not only on waste, but also, for example, on polymer insulation of wires, plastic water supply communications. And this may cause accidents and man-made disasters.
Turtle coming to breathe to the surface in t e iddle o rubbi oatin in t e Atlantic Ocean
A Grey Seal at Horsey Beach in England, tragically caught in a ection o fi in net an u ettin ite t at a re orted to local animal welfare.
M AT E RI A L S S CIE N CE
WINGED ELEMENTS Aluminium, the most widely found metal in the earth’s crust, was generally more expensive than gold half a century ago, although its reserves are hundreds of millions times ampler. The precious aluminium helped the man climb into the sky. However, it seems that soon it may relinquish the title of “winged metal” to titanium and … carbon.
BIOLOG Y
Cell Cultures
BIOLOG Y
How a cell turns into an organism
At the very beginning, we are all just a single cell — the zygote. It forms as a result of merging of two other cells: male and female gametes. The zygote divides, and its direct descendants, cells, look the same for a certain time after the so-called cleavage. Further along, they become the building material for absolutely different organs: brain, heart, bones. How do cells figure out who to become and where to grow?
M E DICIN E
WHAT CAUSES
ALLERGIES? Plasmatic B-cells releasing antibodies
You can feel the spring in the air again! The days are getting longer, the wind doesn’t nip at your nose anymore, snow melts, and streams run down the asphalt in the cities that were so chilly not long ago. But there are people who have to face new challenges when warm spells come. Every year, it’s as though they’re preparing for war: they stock up on drugs, buy medical masks. These are highly allergic people, and spring poses a serious threat to them.
#15 J UNE 2018
51
e rover orn eel are t e ain ri endan erin t e i ion co letion alt ou t eir current tatu fit in t e calculation o en ineer . n all eel o t e device t ere are t ree ori ontal tri it ole ic o t e letter J, P and L (·—— ·—· ·—·· . i i an abbreviation o t e et ro ul ion aborator t e creator o t e rover.
e ar rover fir t elfie a t ta en on ctober on t e 4t da o it ta on ar . an to t e e t e o i a e cienti t on art can detect al unction in t e device.
T ECHNOLOG IE S
S PAC E
DEBRIS The
Kessler
Syndrome
In 1978, the consultant of the NASA’s Environmental Protection Agency Donald Kessler predicted, with a surprising accuracy, the situation the modern astronautics has eventually found itself in. This was the reason scientists immortalized his name in the term “Kessler effect” which describes the impossibility to take advantage of the near space because of orbital debris. Sounds incredible?
T ECHNOLOG Y
Home 1.0. The History of Dwellings OYLA | REAL ESTATE AGENCY
In the beginning, our ancestors lived in… nests. Later they moved to caves and huts from bones. Then they made dugouts in the hills. And then they came one after another: castles, palaces, skyscrapers…
It’s a nest. A most ordinary one made from twigs and grass. Scientists believe that our ancestors, Australopithecus, probably built them like modern anthropoid apes (monkeys with bodies similar to ours) do. Did you know that they lived in nests? Well, not live but rather spend nights. Monkeys are always on the move — they wander from place to place and build a new nest every night. Chimpanzees and orangutans make them on trees, and hefty gorillas set them up right on the ground (tree branches simply break under their weight). Those were not proper dwellings, but merely “beddings.” Real dwellings appeared when our ancestors wanted to make something stronger, more durable, bigger. But why? There are many versions. Among the most convincing is a simple one. The ancestors gradually mastered hunting, and not only gophers and meerkats (mongooses that inhabit the human ancestral home — Africa), but also a larger “catch” began to come into their deft hands. For example, elephants. You can’t eat it at one sitting. What can be done? Right. Share it with a friend. Or rather, with friends — a big family (ancient people lived in groups of 20–30 people). And still, there’s plenty left. And then predators are closing in from all around — they also want a piece of fresh meat. The only solution is to make a feast of feasts. That is, to set up a camp. For a few days, no more (need to go further, keep hunting), but all the same. Branches, stones, straw — anything that is at hand will protect them from predators.
Beginning of Time
SKE P T IC
Hiding From Us Whenever something happens in the world, there is always someone at fault. And if this “something” is on a global scale, it obviously didn’t happen without some kind of conspiracy. Are doctors advising that you be vaccinated? They want to cash in on vaccine sales! A man walked on the moon? Falsification, of course! And worldwide surveillance? We are all in danger … until we turn on our common sense and start thinking critically.
S O CI E T Y
BET ON
TRUTH
Truth, as you know, is born in arguments, and betting on it can also bring a reward. Of course, it is so darn nice to rub it in the opponent’s face with the phrase “I told you!” But getting the prize is also great. And who appreciates the truth more than scientists?
DISCLAIMER We do not promote gambling! You and your friends can argue which of you will go to Mars or receive the Nobel Prize, but it isn’t advisable to bet away the money that’s been put aside for lunch.
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