# Joatmon

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Joatmon had the most liked content!

## Community Reputation

108 Excellent

• Rank
Molecule
• Birthday 12/23/37

## Profile Information

• Gender
Male
• Location
Near Leicester, UK
• Interests
Travel, motoring, Family (Great Grandfather), eating out.
• College Major/Degree
Several colleges (mobile life) - HNC (Electrical and electronic Eng.)
• Favorite Area of Science
Electronics
• Biography
22 years in the British Air Force, 5 years trying this and that, 10 years lecturing at Technical College, early retirement at 55.
• Occupation
Radar Technician (RAF), Military Instructor (Civilian), Computer Customer Engineer, Test Department manager (Civilian manufacturer of Military Electronics), College Lecturer.
1. ## Why do we need vacuum tubes, transistors..why not just use DC?

Question asked - Why even have the power source (wall outlet basically) connected to the VT, and just hook up the power source up to the computer directly, Simple Answer. Wall sockets provide relatively high voltage alternating current, computers run on low voltage direct current, as do most electronic circuits. You need something to reduce the voltage (a transformer) followed by something to change the alternating supply to direct current ( a rectifier). The rectifier back in the 1960's would have used one or more vacuum tubes (thermionic diodes). With the coming of transistor technology the diodes would be replaced by semi-conductor diodes (PN junctions). Later still the development of silicon based devices such as transistors and microchips allowed ever more complicated circuitry to be developed that would hold the low voltage circuit supply steady under different loads and a range of input voltage. We now call a package that contains the three elements(voltage reduction. rectification, stabilisation) a power supply. It usually is a small black box that sits between your wall socket and your computer.

3. ## Fermat's Last Theorem with hardly any Mathematics

Thank you Carrock for considering my ideas concerning Fermat's last theorem. Concerning the points you raise you can plot a sine wave by dividing a straight line of numerical value 1 by any number of fractions, comprise a table of the square root of each fraction and make these the points on your graph. In theory you could use an infinite number of plots for an infinite number of fractions. You can use this data to go up and down and then down and up to produce one cycle of a sine wave. That will cover all possibilities concerning Fermat's mention of integers. I don't understand the comment sin x cannot be greater than 1. I said that the maximum value of sin x was 1 and if all the fractions were multiplied by a greater number you would produce a sin wave with a peak value of that greater number. I'm sorry if my use of IMO put you off. Of course I would like you to look beyond that and let me know where you feel I have gone wrong if you see a misconception. That would be a real help.
4. ## Fermat's Last Theorem with hardly any Mathematics

I don't see a problem, but perhaps the point you raise was why Fermat stipulated integers, not irrational numbers. However if you could get absolutely accurate values for e and pi then the following would, IMO, be true:- One of the sine waves to be added would peak at e times 1 (sine 0 degrees), be e times .707 at 45 degrees and e times 0 at 90 degrees. The other sine wave to be added would similarly peak at pi times 1, be pi times .707 at 45 degrees and 0 at 90 degrees. If these two are in phase and added the resultant would peak at e+pi and if one is phase shifted with respect to the other the resultant waveform will have a lower peak value. When the resultant phase shift is the correct value it will be SQR(e^2 +pi^2). This will happen at a phase shift of 90 degrees. Therefore squaring each side of the triangle will produce a correct sum e^2+pi^2=(SQR(e^2+pi^2))^2. NB *707 is approx SQR(1/2) .
5. ## Fermat's Last Theorem with hardly any Mathematics

Perhaps I should have realised that someone might think he had a possible solution that was 1^n +2^n=10^n! I thought the point was covered in the first line. To be clear I should have asked the reader to also satisfy themselves that in all possible candidates for A^n+B^n= C^n, C will be larger than A or B and smaller than A+B. ,
6. ## Fermat's Last Theorem with hardly any Mathematics

Someone claims to have a whole number solution to A^n+B^n=C^n where n is greater than two. If they have the three numbers then they can form a triangle. This triangle will always have an apex (junction of A and B) which will be less than 90 degrees. Please consider whether you agree with this statement before proceeding! This triangle can be considered as a triangle of forces and from which a parallelogram of forces can be drawn. Using the parallelogram of forces both a vector diagram and a phasor diagram can be drawn and used as reliable tools for navigators and engineers of all disciplines. A phasor diagram can only be used for adding sine waves and they must be of the same frequency. By definition each point on a sine wave is a multiple of the square root of a proper fraction. (opposite divided by hypotenuse) If you plot a graph or create a waveform where each plotted point is something different to the square root of the fraction (say the cube root) you will have a graph that is not a pure sine wave. Only a sine wave has the property of adding two sine waves to make another sine wave. Any other shape of waveform or regularly repeating graph has to be considered as a group of sine waves of different frequencies acting together( fundamental frequency and harmonics). This is Fourier analysis of a waveform. So each frequency that makes up the waveform that is not a pure sine wave, requires its own phasor diagram, hence its own triangle, and you would need to analyse a full set of these triangles to form the final total. But it was stated earlier that a single triangle would suffice! The rather strange conclusion that I come to is that s each side of a triangle, where each side is an integer, is the square root of something and the triangle gives a correct addition of these square roots on a plane surface. Only triangles with an apex angle of 90 degrees will form a a phasor or vector straight line if all sides are squared. The case was made earlier that all triangles that represented A,B,C, in the formula A^n+B^n=C^n where n is greater than 2 will not contain a right angle. That all such triangles can represent a vector or phasor diagram on a plane surface and that the only chance you have of putting the vectors or phasors (which represent sine waves of one frequency) in line is to square each side. It will always fail to do so if the triangle does not contain a right angle. So the rather strange conclusion is that it is only possible to construct a triangle, where each side is the square root of a number. The the only way of using the triangle to represent a sum is to square the sides. If the triangle is right angled we get a correct sum and if the angle is less then 90 degrees we get an incorrect sum.. So, for example a triangle of sides 6,8,9 which seems to almost represent 6^3+8^3=9^3 represents two phasors separated by approximately 110 degrees, which provide the incorrect sum 6^2+8^2=9^2. I see this as strong evidence, perhaps even a logical proof, that Fermat's last Theorem is true by absurdum.
7. ## A question about vibrations and water

Perhaps any gap, or void that has been mentioned would be in the form of water vapour. This seems closely allied to cavitation on ship's propellers. https://www.iims.org.uk/introduction-propeller-cavitation/
8. ## Solving a formula

Can't argue with that I guess that if I got a chance to play chess against a grand master I would jump at the chance and come back for more after losing. I suppose its a question of what one finds interesting or fun
9. ## Solving a formula

That is true and also for other specific values of n. However, perhaps the source of the formula I gave might lead to a generalisation for all values of n. I admit that is unlikely but it is an interesting conundrum.
10. ## Solving a formula

I think that sometimes a journey and its byways can be as interesting as a destination never reached. Also, I feel certain that there are a number of people in the world, such as me, who although knowing they are almost certainly deluded, think that there is just a possibility that there is still to be found a much more simple way of proving Fermat's Last Theorem than that produced by Andrew Wiles'.
11. ## Solving a formula

I'm not surprised - if I have worked things out correctly then a whole number solution would lead to a whole number example of A cubed plus B cubed = C cubed. If it can be proved that there is no whole number solution then it can be concluded that there is no whole number solution to A cubed plus B cubed = C cubed.
12. ## Solving a formula

I have reason to think that if A, B and N in the following equation are positive whole numbers then there is no solution. I would like either values of A, B and N which satisfy the equation or a reason why there is no solution. If you think it looks easy then give it a go - please.