As every holiday New Year has its own attributes. It is even difficult to imagine New Year greeting card or some New Year issue of the newspaper without such items, as Santa Claus , Christmas tree and Christmas decorations, frosted windows and the snowflakes, the clock and the candles.

This time, the newspaper " Kyiv Polytechnic " which is the research university of NTUU "KPI" publishing, decided to issue short story about the three attributes of New Year: the snowflakes, the clock and the candle. Stories are unusual and their authors are remarkable scientists and classics of natural science: Johannes Kepler, Christian Huygens , Michael Faraday. We offer our readers snippets of their songs - " The hexagonal snowflakes " (1611 ), " The Pendulum Clock " (1673 ), " The History of the Candle " (1861).

New Year's gift, or hexagonal snowflake

Johannes Kepler (1571-1630) – is a German astronomer, mathematician and optician. He is known for his discovery of the laws of planetary motion, called Kepler's laws .

To glorious court counselor of His Imperial Majesty , Johann von Mattei Vakgeru Vakenfelsu, golden knight, and so forth, patron of science and philosophy, my lord benefactor .

As I am not aware of how much you love Nothing because of its small value, but because of the magical fun .. It is easy to guess that gift would be more pleasant and desirable for you if it looks like … Nothing

I pass the bridge, tormented by shame over his indiscretion: after I left you without a New Year's gift! And here I are folded opportunity: water steam, compacted from the cold in the snow, snowflakes fall on my clothes, all as one, with hexagonal rays. By Hercules, here's the thing, which is less than any drops, has a form that can serve as a welcome New Year gift lover of anything, and worthy of mathematics that has nothing and receiving nothing, since falling from the sky and carries a kind of hexagonal star!

Because ... every time it starts to snow, the first snowflakes have six-pointed star shape and there must be a reason of it. If it's a coincidence, so why is there no pentagonal or heptagonal snowflakes and why do the hexagonal do not lose their shape and do not clump together but fall apart and far between?

When I have recently spoken with someone about this issue, we agreed that firstly we must consider not the material, but operating principles. Because the substance of snow is steam. Under the influence of some heat from Earth the extracted steam becomes solid and like a liquid and therefore it is not in a form of a star.

If it is determined that the cause of hexagonal shape of snowflakes is connected with their operating principle,we must ask what exactly is that principle, how it operates or is that form initial or acquired by external influences? Whether material accepts hexagonal shape due to the need or naturally? What should be considered an innate: embodied in the hexagonal archetype of beauty or knowledge concerning the aim of such form? To address these issues, we turn to the illustrative examples, but let us consider them geometrically. For our problem such excursus will be extremely useful.

Then Kepler tells about the honeycombs, right rhombic frames, shapes of garnet grains and a pea, about the reason why flowers have five petals and why windows are frosted in winter, many other issues , and …

Finally, a serious conversation about the hexagonal shape of the snowflake. While I was writing these lines it began to snow again, and even more abundantly. I began to examine snowflakes carefully. All of them were with the direct rays but of two types. Some snowflakes were very small with a different number of rays that stuck out in all directions. Those rays were naked, thin and without the edge strips. All the rays were gathered in a little bit bigger ball in the center. The most of snowflakes were of such type. More rare snowflakes of a different kind were scattered among them - hexagonal stars. None of them was similar in shape to another before or after falling on the ground. The fluffs of the stars were placed in the same plane of the ray.

The seventh beam, a shorter one, sticked out downwards like a root, on which showflakes might fall and when having fallen were kept on it for some time. I have noticed this fact during previous observations, but interpreted this incorrectly as if three diametres that form the skeleton of a snowflake do not lie in the same plane. Snowflakes of the first kind are reminiscent of hailstones. as it seems to me, they arise from the steam which is almost devoid of warmth and have begun to thicken in water drops. Therefore they are round, unsightly, deprived of shaping forces, and their central cores are surrounded by the beams because of the same reason that frost is formed on the window…

Concerning the second kind of snowflakes that have the form of a star, they do not look like neither as a cube, or a octahedron, nor as a touch of drops, as these stars fall flat…

But why does just a regular hexagon arise? Is it because of that a hexagon is the only figure among all regular ones from which it is impossible to form a volumetric body? After all, an equilateral triangle, a square, and a regular pentagon form a body. May be the reason that regular hexagons can cover a plane without a single gap? But an equilateral triangle and a square have the same property. Maybe because a regular pentagon come closest to the circle among all regular plane figures, capable of covering a plane entirely, without a gap. Maybe the reason should be sought in the difference between the force that causes infertility and productive force, believing that the former creates regular pentagons and the latter forms an equilateral triangle and a regular hexagon? Maybe, finally, the shaping nature in its deepest essence has to do with a regular hexagon?

Unfortunately, we have to interrupt the story, and hope that readers will appeal to the book of Kepler and learn his answering all the questions. Should be noted that he answered very well - Academician V.I. Vernadsky, a mineralogist by profession, wrote that the first scientific work on crystallography was a little work of Kepler about snowflakes.
Pendular clocks.

Christian Huygens (1629-1695) is Dutch physicist, engineer, mathematician and astronomer, inventor of the pendular clock with anchor escapement, the author of the wave theory of light, the discoverer of the rings of Saturn and its satellites.

15 years past since I published the watch I invented in the brochure. But as ever since I made many improvements in my invention, I decided to put them in a new book. These improvements should be recognized as the most important part of the invention and as its theoretical basis, which has not yet happened. A simple pendulum can not be considered as a reliable and even measure of time, because its fluctuations depend on a swing: large swings require more time than small ones. However, using geometry I found a new, still unknown way of hanging pendulums. I researched the curvature of a curve that is perfectly suited to provide equal time of oscillations of a pendulum. Once I forced the clock pendulum to swing on this curve, the clock escapement became extremely correct and reliable, as shown by tests on land and at sea. The great advantage of this watch for astronomy and navigation can be considered as established. This curve is one that describes the nail in the air, that driven in the wheel rim, when the wheel is rolling. Mathematicians of our time call this curve a cycloid; because of its other various properties it was studied by many scientists, and by me - because of its suitability for measuring time, which I discovered while exploring its using strict methods of science, and being unaware of this applicability. I've already informed some friends knowledgeable in this area about my discovery...

Now I have substantiated it with the most accurate proof and am publishing. I believe, that this evidence is the most important part of the book. I show the usefulness of the application of complex pendulum in clock mechanisms. For studying its nature I fulfilled a research on the swing center, a study that has been done by several scientists, but without much success. I proved here a number of theorems about lines, planes and bodies which, I think, deserve the attention. But before this I give a description of the mechanical clock device and an application of the pendulum in the form most convenient for astronomical purposes.

History of a Candle

Michael Faraday (1791 - 1867) - English experimental physicist and chemist. He discovered electromagnetic induction, laws of electrolysis, the effect of magnetic fields on light diamagnetism, created the first model of electric motor, the first transformer and many others.

I'm going to... put you in these conversations, a number of chemical information that can be connected with the burning candles... The phenomena observed in the burning candles, such that there is no law of nature, which would not have any relation to it. Consideration of the physical phenomena that occur during the burning of candles - is the broad way that can approach you to the study of science. That is why I hope not to disappoint you, choosing my theme candle rather than something newer…

Mr. Field from Lambeth has provided me a great collection of candles and materials from which they are made. Here, first of all, bovine fat, which is called as far as I know, the Russian fat used to produce Mocanu candles. Fat was invented by Gay-Lussac (or someone else who gave him the secret) and can turn to that wonderful stuff that lies next to it - stearin. Due to the invention of stearin current candle - it is no longer fat, ugly subject, which was the former tallow candles - no, it is subject so net that drops which flow from it, do not dirty things and you can scrape off as powder. The method which was used by Gay Lussac lies in following. Firstly, fat is boiled with lime, and goes something like soap. Then he added sulfuric acid, which binds lime, stearin remains with amount of glycerin. Glycerin released during this process is very similar in composition to sugar. This mixture is pressed - here you see a few more or less squeeze bars, from which can be judged as with increasing pressure, resort to excise a growing number of impurities. Absolutely pressed mass melted, and it cast those candles that I will show. Here is the candle - stearic, it made by the following methods. But spermaceti candle made from a certain sort of whale oil. Here refined yellow beeswax and that also goes for making candles. Paraffin is another interesting ingredient. But paraffin candles made from extracted in Irish bogs paraffin. And I have another substance, something like wax, which sent me kindly one of my friend. It was brought from Japan. This is also a material for making candles.

But how made these candles? I have already told you about the candle Mocanu, and now tell you about the formation. Imagine that some of these sorts of candles made from this material, which can be cast into the form. "Cast?" - You ask. "Well, of course - because candles melt, and if they can melt, they probably can be cast in the form." It turned out that you can. The strange thing here and there, as in improving production and in developing the best means to achieve a particular goal, faced with facts that apparently cannot be predicted in advance. So, the candle cannot always be cast into forms, wax candles, in particular, it is impossible to cast: they are made in a special way, which I will briefly tell in a few minutes…

Let us talk about a candle flame. Light one or two candles, that will force them to do their usual work. As you can see, the candle - not that lamp. The tank in lamp is filling with liquid oil, dip the wick into it with moss or treated cotton, and then lights the tip of the wick. When the flame goes down on wick to the oil, it pales there, but on top continuing to burn. You will surely ask - how oil which does not burn, gets to the top of wick, where it can burn? Later we will examine this phenomenon, however, when candles burning, there is another, even more strange circumstance. After all, before you is solid, so hard, that it is not need utensils. And how can this solid rise to the point where is flame? How this solid get there without being a liquid? On the other hand, how it does not spill when converted into liquid?

Unfortunately, we cannot reprint in a newspaper at least one Faraday lecture- it would have taken two of our column. There are six lectures. They tell about the need for combustion of air, and water formation during burning and oxygen, and hydrogen which are in the composition of candles, and that the burning of hydrogen is converted into water, which includes and oxygen, and that oxygen is in the air, and the carbon dioxide that is produced during burning, and finally, the breath and its similarity to burning.
And the last one - sixth - Faraday lecture ended with appeal to listeners :"I can only express my wish that you could sustain honorably comparison with a candle, that would be a beacon to others, and that all your actions you have followed the beauty of the flame, honestly and efficiently performing your duty to humanity".

The same editorial wishes to readers!

By W. Ignatovych