Had too much to dream last night
Chatter #
Attila read Chatter, and enjoyed it very much. I started practcing the tools, and saved the Tools section.
Attila struggles reading formulas! 😌 Tetrahedral numbers
∏_i=n!?
You can practice the Arrowsmith exercise of recalling symbols with closed eyes, or perhaps even with open eyes, as if watching a photograph appear from photosensitive paper.
$\prod_{i=1}^{n} i = n!$
How many different combinations of three AM stations can you choose from twenty-four? $Te_26 = {24 \choose 3}$
How many different combinations of five FM stations can you choose from fifteen? $Te_17 = {15 \choose 3}$
$Te_n = \frac{n(n+1)(n+2)}{6}$
There seems to be a pattern there!
$Te_{17} = \frac{17 \times 18 \times 19}{6}$
$Te_n = \binom{n+2}{3} = \frac{(n+2)!}{(n-1)! 3!}$
Except Attila does not yet see it.🤔
It makes you wonder if the computer agent was using the accurate formula. If 24C3 corresponds to the 27th tetrahedral number, it might make more sense to write ${n-2} \choose {3}$.
I love it! ❤️
The Pythagorean Approach to Problems of Periodicity in Chemistry and Nuclear Physics -D. Weise Awesome article!
You can calculate it using a formula, or even a calculator, plugging in values, and it will spit out some number. 3C3 = 1. It is very intersting, on the other hand, to know, that 3C3 is the number of ways you can play three notes at the same time, on the guitar. Factorials can be drawn with tree diagrams, on which you can see the patterns of variations and combinations. What is the pattern of the multiple of two binomial coefficients? I already have a vague mental image of it, but it would help to see many different visual representation of it. As I learn mathematics the notation starts to make sense, but the abstract notation, and nomenclature initially often felt inaccessible. Multidimensional thinking seems to contribute to accessing it.
Cool links #
- Previous: Learning Gregorian chants and Tibetan om
- Next: Proofs that count