### Calculating, rather than experimenting to find, resistor values for the NTX2 voltage divider

A previous blog post showed the voltage divider circuit I'm using to drive the Radiometrix NTX2 transmitter in GAGA-1. And another blog post gave a spreadsheet for working out the voltages based on resistor values.

What you really want, though, is a way to say "given this required frequency shift what should the resistor values be?". Recall the circuit diagram I was using.
```Arduino                         Radio
7 ---27K--------------\
---------- TX
8 ---22K----2K2-------/
```
Now, replace the specific resistances on the left with R1 and R2 and the input impedance to ground with 100K (the value from the datasheet):
```Arduino                      Radio
7 ---R1--------------\
----------100K---Gnd
8 ---R2--------------/
```
Pins 7 and 8 are connected to either 5V or Gnd to make the divider so you have two configurations:
```Arduino                      Radio
5V  ---R1--------------\
----------100K---Gnd
Gnd ---R2--------------/

Gnd ---R1--------------\
----------100K---Gnd
5V  ---R2--------------/
```
In both cases you can see that one of R1 or R2 is in parallel with the 100K input impedance so the dividers look like (I've used || to indicate the resistances in parallel):
```5V  ---R1--------------X----------R2||100K---Gnd

5V  ---R2--------------X----------R1||100K---Gnd
```
Where the X is the connection to the TX pin and hence where we need specific voltages. For a 425Hz shift the difference between the two voltages needs to be 3/5000*425 (since the NTX2 has a deviation of 5kHz driven by a 0 to 3V value). Thus you can derive the following formula for the difference between the two voltages.

This simplifies to the following when you assume that R1 and R2 are positive (they are resistors after all!)

And that's a rather simple formula relating the resistances. Here's a graph of it (all resistance values are in k).

The cross hairs there correspond to one 22K resistor and another at about 24K2. Of course, if the input impedance isn't precisely 100K this isn't going to work, but the general method will.

### Your last name contains invalid characters

My last name is "Graham-Cumming". But here's a typical form response when I enter it:

Does the web site have any idea how rude it is to claim that my last name contains invalid characters? Clearly not. What they actually meant is: our web site will not accept that hyphen in your last name. But do they say that? No, of course not. They decide to shove in my face the claim that there's something wrong with my name.

There's nothing wrong with my name, just as there's nothing wrong with someone whose first name is Jean-Marie, or someone whose last name is O'Reilly.

What is wrong is that way this is being handled. If the system can't cope with non-letters and spaces it needs to say that. How about the following error message:

Our system is unable to process last names that contain non-letters, please replace them with spaces.

Don't blame me for having a last name that your system doesn't like, whose fault is that? Saying "Your last name …

### All the symmetrical watch faces (and code to generate them)

If you ever look at pictures of clocks and watches in advertising they are set to roughly 10:10 which is meant to be the most attractive (smiling!) position for the hands. They are actually set to 10:09.14 if the hands are truly symmetrical. CC BY 2.0image by Shinji
I wanted to know what all the possible symmetrical watch faces are and so I wrote some code using Processing. Here's the output (there's one watch face missing, 00:00 or 12:00, because it's very boring):

The key to writing this is to figure out the relationship between the hour and minute hands when the watch face is symmetrical. In an hour the minute hand moves through 360° and the hour hand moves through 30° (12 hours are shown on the watch face and 360/12 = 30).
The core loop inside the program is this:   for (int h = 0; h <= 12; h++) {
float m = (360-30*float(h))*2/13;
int s = round(60*(m-floor(m)));
int col = h%6;
int row = floor(h/6);
draw_clock((r+f)*(2*col+1), (r+f)*(row*2+1), r, h, floor(m…

### The Elevator Button Problem

User interface design is hard. It's hard because people perceive apparently simple things very differently. For example, take a look at this interface to an elevator:

From flickr

Now imagine the following situation. You are on the third floor of this building and you wish to go to the tenth. The elevator is on the fifth floor and there's an indicator that tells you where it is. Which button do you press?

Most people probably say: "press up" since they want to go up. Not long ago I watched someone do the opposite and questioned them about their behavior. They said: "well the elevator is on the fifth floor and I am on the third, so I want it to come down to me".

Much can be learnt about the design of user interfaces by considering this, apparently, simple interface. If you think about the elevator button problem you'll find that something so simple has hidden depths. How do people learn about elevator calling? What's the right amount of informati…