Why does n! for big n end at an increasing number of zeros?

Explain why n! (the factorial of n) ends at more and more zeros when you increase n as demonstrated in the following table, the first ending zero is introduced at 5! the second at 10! and this trend will increase for higher n.

For instance, n=18, n! = 18! = 6.402.373.705.728.000 ends at 3 zeros. The question is now why we see this phenomenon. To solve the problem compute all factors for each contribution to the product 1*2*3...(n-1)*n. Sort the factors and take the minimum of the number of factors equal to 2 and 5 in the set of all prime factors; that minimum is the number of ending zeros in n! In this way you learn that for n=10000 the factorial n! has 2499 ending zeros, see the code and the example hereafter. Any ending zero can only happen when the factors of 2 and 5 meet to form a 10, so that you multiply by 10, which adds a zero that will never go away.

Matlab demonstration script
This is what it shows

Note that we did not need to compute n! itself, but only the sum of all the logarithms; the main work is to compute the factors of all integers between 2 and n and to count the factors of 2 and 5.

Last update: 17-Jul-2020 at 12:18

NEOWISE 12-jul-2020

You can do this with the standard iPhone software, it has a 3s averaging mode and that is good enough for capturing it.

This was at 2AM north of Rotterdam The Hague airport, unfortunately there is a bit of light pollution, one of the instagram filters added some blue to the sky. We are looking north.

Last update: 12-jul-2020

Grimeton SAQ transmission

I’ve made a video of what I received on Sunday 5-Jul-2020.

The transmitter is running at a very low frequency of 17.2 kHz, you can’t hear it because it is an electromagnetic wave and not a sound wave. Once or twice per year the machine transmitter is turned on, the most recent event was on 5-Jul-2020. In fact it is a machine transmitter meaning that an engine is generating the RF signal. In 2022-2024 this was meant to be an alternative for underseas telegraph cables. More details about what SAQ can be found on wikipedia

How many fit on 30 by 30 meter?

During times of a lockdown I mentioned this on the PI3RTD repeater, we do radio rounds every day and my question was, “how many persons would fit on an imaginary field of 30m by 30m while we should observe the social distancing rule of 1.5 meter?” My initial guess was 508 because it is close to 30*30/(pi*r*r) where r=75cm, the answers that I received varied between 440 and 583; but in reality there are two answers:

  • 462 if you don’t allow people to stand on the edges of a field
  • 492 if you allow them also on the edges and corners.

Check this yourself, or even better, send me a photo where you’ve practiced this with your local club:

25AD2563-AF25-49A1-A0EF-94F225809FC1
This is 492 persons on a field of 30 by 30m while observing 1.5 meter distance.

Last update: 27-May-2020

 

Antenna situation at JO20vx

Since 8-May-2020 I’m quite more often QRV from JO20vx (actually it is JO20WX04 since this is apparently a boundary between two maidenhead locator regions), in the city of Geleen in The Netherlands because of health care duties. One advantage of this location is that there is a 30m long garden that is about 7 meters wide, so there are plenty of opportunities to play with different antennas in a low noise environment. I can carry two (or three) sets of fiberglass mast elements with me while going here, and whatever fits in the car.

Setup 1: a mast in the center of the garden and a 20 and 40 m band antenna, getting everything 10 meter off the ground is a challenge

Setup 2: a smaller pole in the garden, few meters closer to the house, it is doable but the antennas at too low, will try it in the future with a delta loop.

IMG_0180
The idea is nice, but this secondary mast/pole is too low, the other mast elements are but to get above a tree right behind me.

Setup 3: tall pole at the end of the garden, and a g5rv to one of the chimneys on the house, benefit is that it somehow works

IMG_0197

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This is the better way to do it, a tall mast at the end where a metal gate is used as a support, and a G5RV to the roof

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From the second floor looking down on the garden

Typical setup, ft857d, travel tuner, 3 way coax switch so you can switch between the SDR, the radio and an antenna analyzer. The SDRplay rspduo is for band monitoring.

IMG_0200
Modifications: get ethernet cable upstairs and free this plank to work on.

More recently the set-up was changed, got a FTDX101d which is a really nice transceiver, at a later point in time I will write an article about it.

Last update 5-June-2020

Counting is fun

Decimal, hex, octal, binary, Gray and BCD compared (left), including a rotary encoder setup (right)

counting_is_fun

Note the difference between counting in binary and in Gray code, the latter is used in rotary encoders and digital modulation. Try to understand rotary encoders and connect one to an Arduino, as you can read here

1:6 Balun, 50 to 300 Ohm

The design comes from F6GWO and it turns out to be useful for transforming a 300 Ohm symmetric transmission line to a 50 Ohm asymmetric coax cable. I made it with the available material in the shack, and measured the SWR when the symmetric side is terminated with a 300 Ohm resistor:

IMG_0144
How to make it

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Testing the reflection with a MetroVNA

balun6
Observed SWR against Frequency, so it is good enough, maybe the 80m band and frequencies beyond 30 MHz should be avoided, this may be due to the quality of the ferrite core.

In reality 300 Ohm antennas are typically folded dipoles and delta loops etc. This balun could be useful for a receiving antenna’s, don’t think it will be able to withstand a lot of power and I didn’t intend to test that.

Last update: 6-May-2020

Speaker wire dipole

I’m on travel, have a laptop and a sdrduo with me, but there is no antenna in this house. Ran to the local store and got 100 meter of loudspeaker cable, and it is really all you need to make an antenna to listen to shortwave.

Just make a dipole with arms as long as the garden allows, and use the loadspeaker cable as transmission line. It will work because the impedance of this cable is around 75 to 100 Ohm, there will be impedance differences but around 7 MHz you should have a match with two dipole arms of 10 m. Use anything that you can find to secure the T part of this construction (use rope, wire straps, tape, etc)

They sell this as 0,75 mm loudspeaker cable, cut off 20 meter, split it in two parts, adjust until it somewhere fits in the garden, and use the remaining speakercable as transmission line
Add some rope at both ends and let it run from the roof to a tree in the back of the garden, the wire shouldn’t touch anything, that would probably deteriorate reception quality
Connect the cable to the P and the N of the Hi-Z of the rspduo and there you go. The impedance of the Hi-Z port should be 1 K Ohm, at the moment this is not too important.

Noise levels at this place are fortunately pretty low, there is no need for anything fancy. The speaker cable dipole is good enough to listen to the HF which was the intention of this project.

Here I compare my reception against the University of Twente websdr. This project is not a bad deal, think it is even more sensitive than the websdr.

Last update: 3-May-2020