Heather Nesheim  -  https://www.etsy.com/es/people/heddarsketch  -  https://twitter.com/heddarsketch

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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 

Leap Day…Why Does It Exist?

Once every four years, an extra calendar day is added: a leap day. But why?

The reason for adding leap days to the calendar is to align the calendar year with the actual year – which is defined by the time it takes Earth to circle the sun. It is equal to 365 days, 5 hours, 48 minutes and 46 seconds, or 365.24219 days.

If all calendar years contained exactly 365 days, they would drift from the actual year by about 1 day every 4 years. Eventually, July would occur during the northern hemisphere winter! Wouldn’t that be weird?

To correct (approximately), we add 1 day every 4 years…resulting in a leap year.

By making most years 365 days but every fourth year 366 days, the calendar year and the actual year remain more nearly in step.

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Snuggly boy and his favorite toy.

Video by Marielle Tepe

Extremely Rare Fossil Turtle - Green River Formation, Rocky Mountains, USA

Fossil turtles from the Green River Formation are extremely rare. This is a well preserved, fifty million-year-old Trionyx softshell turtle in limestone. It was found in the upper layers of the F-1 Green River Formation. The stone also contains 9 small Knightia eocaena and a small Diplomystus dentatus.

Alberto Camara  -  http://camarasketch.tumblr.com  -  https://society6.com/albertocamara/prints  -  https://www.instagram.com/camarasketch  -  https://camarasketch.deviantart.com  -  https://twitter.com/Camarasketch

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