> Do you think this accurately reflects the working conditions of a developer?

That's not the goal of the exercise however, nor is it a desirable one. The point is to a very loose test of basic ability. You can test the basic ability of a runner by asking them to do a quick sprint; the fact that this is not an accurate simulation of a race is irrelevant.

> do you think that they will be comfortable making those small errors in front of peopl

They should be. Any programmer should be comfortable making errors and owning up to them.

> Do you think that they jump into problems and that small errors are OK to them
In this situation it is. In a "real world" situation, those would be caught by the compiler or unit tests. Of course really bad mistakes in this test would count against you.

> They may blank, they may freeze

Of course, this can happen in any type of interview. The point of interviews is to try and get the best balance of weeding out unsuitable people and finding the best ones. No matter what process you use, you will occasionally discard perfectly viable candidates...however this is preferable to accepting unsuitable ones.

> just be the type of person that reflects on an issue for a while before the set out to code.

...and that's fine...I'm not sure why you think this is some sort of "gotcha" test. It's perfectly fine to take some time...nobody is timing you. Again, this is a basic test to make sure you have the simplest skills and to get a little insight into your thinking/working. If you are uncomfortable with some aspect of the test, it is fine to say "well usually I take some time to think" or "I don't like writing on whiteboards"...etc.

You seem to be fundamentally misunderstanding the nature and point of the exercise. Errors are ok and expected because it's a simple test of reasoning and logic ability...likewise jumping in is ok because it's a simple problem.

Do you as a programmer spend a lot of time considering a simple if/else statement? Of course not...you jump in and write it. Again, we are talking about a simple algorithm here...given the description it basically writes itself for anyone with a modicum or programming experience.

The point here is to get a basic assessment of raw ability. The rest of the interview is to determine how well they might fit in the company, and any other gaps can be filled in with training.

> I personally would search for the mathematical formula and a text description that I could put on my second monitor as reference

That's the point you're missing. You don't need to search for that, it's been given to you. The description of the triangle contains the algorithm for constructing it. It's also so simple that you should be able to hold it in memory for the short time necessary, but if needed you could ask for a refresher.

> But first I would search for a standard library and avoid the effort all together.

That would negate the purpose of the test. Again, this is the most basic of basic programming tasks. It tests your ability to write simple logic and flow controls...something fundamental to writing computer programs.

Even if you solve a problem using mostly library functions, you still will need a few simple loops and logic to tie them together, and that's what this is testing.

> I personally never work from verbal descriptions

The verbal here is incidental...the point is you're working form some description or set of requirements. In this instance it's so simple that a verbal description will suffice, perhaps with one or two reminders. If you really can't hold such a simple description in your mind for 20 minutes I'd say you're not suited for any sort of mental work and might need to see a neurologist.

It seems your objections are based on a flawed premise, a fundamental misunderstanding of what the test is, how simple and easy it is, and what it is supposed to be testing.

If you look at want ads for day labor and other physical tasks it will often say something like "must be able to lift 50 lbs". When you went to the job site, they might ask you to lift a bag of concrete weighing 50 pounds. This is an exceedingly simple task and anyone fit for the job will be able to do it easily. It will quickly weed out anyone who is simply unfit for the work required, anyone who is fit will be able to do it easily.