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Long division
Long division is a method of dividing two numbers, using repeated multiplications and subtractions in a tableau. Because it is easy to do, it is usually taught in schools. There are other methods which are faster, or easier to program with a computer, but they are more difficult to understand and perform manually. If we have a large or complicated division problem, we can use long division to break it down into a series of easier calculations. Long division can also be done on polynomials as well.
As with most division problems we have three numbers: the dividend, our first number; the divisor, the second number we divide it by; and the quotient, which is the result. Long division is a kind of algorithm, which means it helps us to find the solution to a problem by following a set of clearly-defined steps:
Let's assume we want to divide 780 by 4. To do so with long division, we need to split 780 into digits -- 7 and 8 and 0 -- and then divide each one by 4, carrying any remainders to the next step.
7 / 4 = 1 R 3 -- since we have a remainder of 3, we have to carry this down.
38 / 4 = 9 R 2 -- we carry our remainder of 2 down.
20 / 4 = 5 R 0 -- we have reached the end.
By using long division, we have found that 780 / 4 = 195.
Let's perform a similar calculation where our numbers do not divide easily: 468 / 12
4 / 12 = 0 R 0 -- we cannot perform this division as 4<12, so we have to carry our dividend like a remainder.
46 / 12 = 3 R 10 -- we carry our remainder of 10 down.
108 / 12 = 9 R 0 -- we have reached the end.
By the same process we have found that 468 / 12 = 39.
Let's follow the same process for numbers that give an answer with a decimal because they don't have common factors: 123 / 8
1 / 8 = 0 R 0 -- we cannot perform this division as 1<8, so we have to carry our dividend like a remainder.
12 / 8 = 1 R 4 -- we carry our remainder of 4 down.
43 / 8 = 5 R 3 -- we have reached the end with a remainder, which we have to add to our final answer.
123 / 8 = 15 R 3, which equals 15.375 (15 3/8).
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Philipp Lenard
Philipp Eduard Anton von Lenard (7 June 1862 – 20 May 1947) was a Hungarian-born German physicist. He won the Nobel Prize for Physics in 1905 for his work on cathode rays. His most important work was his study of the photoelectric effect. He discovered that the energy (speed) of the electrons from a cathode depends on the wavelength, not the intensity of the light.
Lenard was a nationalist and anti-Semite. He was a supporter of Adolf Hitler in the 1920s. He was a role model for the "Deutsche Physik" movement during the Nazi period. He said that Albert Einstein's contributions to science were "Jewish physics".
Philipp Lenard was born in Pressburg (today's Bratislava), on 7 June 1862 in the Kingdom of Hungary. The Lenard family were of German-descent. His father, Philipp von Lenardis (1812–1896), was a wine-merchant in Pressburg. His mother was Antonie Baumann (1831–1865). In 1880, he studied physics and chemistry in Vienna and Budapest, going back to Pressburg in 1882. After being refused an assistant's position in the University of Budapest in 1883, he moved to Heidelberg. He studied under the Robert Bunsen, and also one semester in Berlin with Hermann von Helmholtz. He gained a doctoral degree in 1886. In 1887 he went back to Budapest to work for Loránd Eötvös. After working in Aachen, Bonn, Breslau, Heidelberg (1896–1898), and Kiel (1898–1907), he went back to the University of Heidelberg in 1907 as the head of the Philipp Lenard Institute. In 1905, Lenard became a member of the Royal Swedish Academy of Sciences. In 1907, he became a member of the Hungarian Academy of Sciences.
He studied phosphorescence, luminescence, and the conductivity of flames.
Lenard began the study of cathode rays in 1888. These rays were made in simple, partially evacuated glass tubes. Inside were metallic electrodes across which a high voltage could be placed. It was difficult to study the rays inside the sealed glass tubes. They were difficult to access, and and there were still air molecules in the tubes. Lenard was able to make small metallic windows in the glass, thick enough to be able to withstand the pressure, but thin enough to let the rays pass through. He could pass the rays out into the laboratory, or into another chamber that was completely airless. These windows are now known as "Lenard windows". He could easily detect the rays and measure their intensity by using paper sheets with a layer of phosphorescent materials.
Lenard saw that the absorption of cathode rays was proportional to the density of the material they passed through. This was opposite to the idea that they were some sort of electromagnetic radiation. He also showed that the rays could pass through the air and appeared to be scattered by it. This meant that they must be particles that were even smaller than the molecules in air. He confirmed some of J.J. Thomson's work, and this showed that cathode rays were streams of negatively charged energetic particles. He called them quanta of electricity or for short quanta, after Helmholtz. J.J. Thomson had called them corpuscles, but electrons became the everyday term. Lenard used this knowledge, together with the results of his and others' earlier experiments on the absorption of the rays in metals. He showed that electrons were parts of the atom. Lenard worked out that atoms were mostly empty space. He said that every atom consists of empty space and electrically neutral corpuscules called "dynamids", each consisting of an electron and an equal positive charge.
He experimented using a Crookes tube. He showed that the rays produced by irradiating metals in a vacuum with ultraviolet light were like cathode rays. He found that the energy of the rays was independent of the light intensity, but was greater for shorter wavelengths of light.
Albert Einstein explained this as a quantum effect. This theory said that the plot of the cathode ray energy versus the frequency would be a straight line with a slope equal to Planck's constant, "h". This was proved some years later. Einstein was awarded the Nobel Prize in Physics for this theory. Lenard did not like the attention given to Einstein. He did not believe in Einsteins theories, including relativity. However he did agree with Einstein's explanation of the photoelectric effect.
Lenard received the 1905 Nobel Prize for Physics in recognition of this work.