Most of this is is flavour, with a section of puns setting the scene at the start, and then the story itself in the middle. Scroll down for the actual puzzle. You may be interested to know that all the facts about the brain are true.
Everything in this story is true, except for the bits that aren't. That's probably not very helpful...
Someplace, somewhere, at exactly sometime before noon, there is a building which specialised in doing just one thing: being a hospital, university and medical research facility.
This medical building employed people. It employed chemists in their element, physicists of little matter and biologists studying blood cells, but in vain.
It made sure it didn't employ poets. The building had decided that anyone who writes inverse must be a backward person.
It did however employ mathematicians, the small fraction of the world who knew there was a fine line between a denominator and a numerator.
One of these mathematicians was employed as a maths teacher for the university students. He was such a good teacher, he actually could control the class and teach them things. He wasn't like the cross-eyed teacher down the corridor who couldn't control his pupils. He wasn't like the teacher in the room opposite who was rather average because he was so mean. And he definitely wasn't like the teacher upstairs who had problems which showed the first sine of madness. No, this teacher was a good teacher. He was also a doctor, and he was very good at that too. He never lost his patients.
Today he was teaching his students about mathematical fallacy. Quite illogical if you ask me.
The teacher turned and wrote What is 1+1? on the blackboard. He turned to the class and asked what was the answer. Someone shouted out "2!".
"Alright then, let me prove it equals 1."
He turned back to the blackboard and wrote the following:
Now he looked at the class and was about to point out the mistake, where dividing by (a-b) is dividing by zero. He was though interrupted as a panting doctor burst into the room.
"Dr, Patient 3145 is awake and walking round the hospital."
The class stirred. Everyone had heard of Patient 3145. No-one knew who he was, just that he had been trapped in an icy lake and suffered extreme brain damage. The doctors, including the teacher, had tried some experimental treatment on him and it had worked. But with some side effects.
During his coma, his brain had shown signs of hyperactivity. His treatment had greatly increased the rate of neurogenesis, usually very small in adults, and as a result, instead of losing around 7000 neurons per day, the average amount for an adult over 20, he was gaining a couple of thousand. This in turn was opening up new neural pathways, allowing quicker thought and reactions, more control of the body and the ability to multitask. Not only this, but his axons were firing quicker across synapses, neurotransmitters moving faster and information being transferred quicker. He was now estimated to be the most intelligent human in history.
On the few times he had woken, he hadn't done that much, but he had shown signs of heightened intelligence.
In the end however this treatment would be a failure. The reproduction of brain cells was causing immense pressure on his brain, which would eventually shut itself down.
But now it seems he had woken and had gained enough strength to walk. And as if on cue, he walked into the classroom.
Everyone fell silent watching him. He walked up to the board, looked at it for a second, then picked up a chalk. For a few seconds no-one could see what he was drawing, but then he stepped away and walked out of the room to reveal a beautifully intricate pattern:
(Click for a larger image of the main pattern, image has been updated to give a hint and to fix an error)
The students nor the teacher could work out its message. Maybe you can?
What does 1+1=?
This will be helpful for spotting something in the puzzle indicating the next step (Now Solved)
Hint for last step:
Something like Excel can create something useful to do with what ChrisHappy found in his answer (3x16) which can be filled with information from the triangles. Then you have the final answer.
Try filling a 3x16 grid in with the triangles