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Mathematical Curiosities

                                   More number patterns

  With 9s we can produce another aesthetically pleasing pattern shown below. 

                                         999,999 · 1 = 0,999,999

                                         999,999 · 2 = 1,999,998

                                         999,999 · 3 = 2,999,997

                                         999,999 · 4 = 3,999,996

                                         999,999 · 5 = 4,999,995   

                                         999,999 · 6 = 5,999,994

                                         999,999 · 7 = 6,999,993

                                         999,999 · 8 = 7,999,992

                                         999,999 · 9 = 8,999,991

                                         999,999 · 10 = 9,999,990

Here is another number pattern, where the number 9 is multiplied by a number representing the consecutive natural numbers- increasing by 1 each time- and then added to the initial natural numbers consecutively. 

                                                   0 · 9 + 1 = 1

                                                   1 · 9 + 2 = 11

                                                 12 · 9 + 3 = 111

                                               123 · 9 + 4 = 1111

                                             1234 · 9 + 5 = 11111

                                           12345 · 9 + 6 = 111111

                                         123456 · 9 + 7 = 1111111

                                       1234567 · 9 + 8 = 11111111

                                     12345678 · 9 + 9 = 111111111

We can consider number patterns that can be generated in a similar fashion, yet somewhat in the reverse of the previous one. However, this time the generated number consist of all 8s. 

                                                  0 · 9 + 8 = 8

                                                   9 · 9 + 7 = 88

                                                 98 · 9 + 6 = 888

                                               987 · 9 + 5 = 8888

                                             9876 · 9 + 4 = 88888

                                           98765 · 9 + 3 = 888888

                                         987654 · 9 + 2 = 8888888

                                       9876543 · 9 + 1 = 88888888

                                     98765432 · 9 + 0 = 888888888

Now that we have introduced the 8s in a rather dramatic fashion, we shall use them as the multiplier with the numbers consisting of increasing natural numbers, and each time adding successive natural numbers. Appreciating the number pattern shown here is more pleasing than trying to explain this phenomenon, which could conceivably detract from its beauty. 

                                                  1 · 8 + 1 = 9

                                                12 · 8 + 2 = 98

                                              123 · 8 + 3 = 987

                                            1234 · 8 + 4 = 9876

                                          12345 · 8 + 5 = 98765

                                        123456 · 8 + 6 = 987654

                                      1234567 · 8 + 7 = 9876543

                                    12345678 · 8 + 8 = 98765432

                                  123456789 · 8 + 9 = 987654321

Content credit: Mathematical Curiosities A Treasure Trove of Unexpected Entertainment 

Piotr Rajchel

The concept of information as viewed in theoretical physics through statistical mechanics and thermodynamics, and its implications and connections with evolutionary biology. An interesting reading:

How Life (and Death) Spring From Disorder (via WIRED -original story from Quanta Magazine)

Biological systems don’t defy physical laws, of course—but neither do they seem to be predicted by them. In contrast, they are goal-directed: survive and reproduce. We can say that they have a purpose—or what philosophers have traditionally called a teleology—that guides their behavior.

By the same token, physics now lets us predict, starting from the state of the universe a billionth of a second after the Big Bang, what it looks like today. But no one imagines that the appearance of the first primitive cells on Earth led predictably to the human race. Laws do not, it seems, dictate the course of evolution.

–

David Kaplan explains how the law of increasing entropy could drive random bits of matter into the stable, orderly structures of life.

Sellos

Se utilizaban para estampar diseños sobre materiales perecederos como la tela y el papel o para decorar cerámica.

INAH

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