@Gabby Tau is indeed a remarkable number that we would all do well to contemplate and celebrate. It has the property of being always exactly twice the length of Pi no matter how large or small the circle is that contains it.

That there is such a constant relationship between these two mysterious universal numbers is itself a mystery worthy of great contemplation. For although modern science has the enduring wish to say that all things in our minds have come about by the blind blunderings of Evolution – yet surely not even the most dyed-in-the-wool scientist would try to claim that Pi and Tau are the products of Evolution.

Yet as they are not products of Evolution we can simply all acknowledge that therefore by simple logic that there must be Creative Forces that are not Evolution.

Whether these are the Creative Forces as foretold by the Vedas or experienced by our deepest Shaman is of course not something that can be deduced from the sole contemplation of the relation between Tau and Pi. Yet such considerations themselves are of great value if we allow our meditative insight to inform our rational enquiries.

And thus an apparent simple geometric relationship can be a key to unlocking the door to a glimpse of true cosmic harmony and our origins as conscious beings set forth upon this universe.

Thanks Gabby for introducing me to this number and prompting me to do further research. However, much as I appreciate the benefits that can be obtained by using tau in certain places I feel I must pledge my allegiance to pi for at least a couple of reasons:
* on a practical note, it is easy to measure the diameter of a pipe or a wheel, whereas measuring the radius is harder if not impossible
* on a theoretical note, the elegance of the equation e ^ i*pi = -1 just doesn’t resonate the same way with tau

The numbers 1 up to and including 16 can be placed in sequence in such a way, that the sum of each two consecutive numbers is a square. How should this be done?

Started with 16 and worked backwards. I think there was only one point where there were two possible next numbers. (3 could be followed by 1 – but that crashed a few numbers later),

Happ TAU Day to us all – a rational alternative to PI for all aspiring mathematicians and geometers.

@Gabby Tau is indeed a remarkable number that we would all do well to contemplate and celebrate. It has the property of being always exactly twice the length of Pi no matter how large or small the circle is that contains it.

That there is such a constant relationship between these two mysterious universal numbers is itself a mystery worthy of great contemplation. For although modern science has the enduring wish to say that all things in our minds have come about by the blind blunderings of Evolution – yet surely not even the most dyed-in-the-wool scientist would try to claim that Pi and Tau are the products of Evolution.

Yet as they are not products of Evolution we can simply all acknowledge that therefore by simple logic that there must be Creative Forces that are not Evolution.

Whether these are the Creative Forces as foretold by the Vedas or experienced by our deepest Shaman is of course not something that can be deduced from the sole contemplation of the relation between Tau and Pi. Yet such considerations themselves are of great value if we allow our meditative insight to inform our rational enquiries.

And thus an apparent simple geometric relationship can be a key to unlocking the door to a glimpse of true cosmic harmony and our origins as conscious beings set forth upon this universe.

Thanks Gabby for introducing me to this number and prompting me to do further research. However, much as I appreciate the benefits that can be obtained by using tau in certain places I feel I must pledge my allegiance to pi for at least a couple of reasons:

* on a practical note, it is easy to measure the diameter of a pipe or a wheel, whereas measuring the radius is harder if not impossible

* on a theoretical note, the elegance of the equation e ^ i*pi = -1 just doesn’t resonate the same way with tau

Re paragraph 1, pi is not a length. It is a ratio of two lengths.

The numbers 1 up to and including 16 can be placed in sequence in such a way, that the sum of each two consecutive numbers is a square. How should this be done?

8 1 15 10 6 3 13 12 4 5 11 14 2 7 9 16

Clever. How did you do it?

Started with 16 and worked backwards. I think there was only one point where there were two possible next numbers. (3 could be followed by 1 – but that crashed a few numbers later),