Pythagoras: One of the Greatest Minds of His Time

Pythagoras was one of the greatest minds and philosophers of his time and his unquestionable influence can be felt even today in mathematics. He was the founder of Pythagoreanism, a religious and political movement that appeared mainly in the big cities of Magna Grecia. He dedicated his life to the spiritual and moral awakening and reformation of people from all social classes and sexes. Thus, Pythagoras was one of the most open-minded thinkers of his era.

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Finally motivated myself to start on math to prep for the upcoming school year and i lost my study stamina :( [used to be able to sit for hours studying] my brain is pretty much fried to do anything else now.

Not the prettiest notes/work/handwriting you’ll see around here but just wanted to post something and keep this blog active while i can during the holidays.

Vote on which topic you want to see covered next!

I’m planning a few posts in the near future, but I’m wondering which topic interests people more.

The topics I’m considering:

  • Mirrors of different shapes: I’ll explore how rays and waves are reflected by different shapes, and some interesting properties of these shapes. I have more ideas beyond the typical parabolic/elliptical/spherical mirrors, so I’m sure there’ll be more than the usual here.
  • Bees & voting systems: I’ll explore alternative voting systems being proposed, but from a less techy & more intuitive and visual perspective. I’ll also explain how bees have been using a system for millions of years and trillions of elections, and what we may be able to learn from them.
  • Snowflakes: I’ll explore current research on how snowflakes are formed, what causes their symmetry and, hopefully, have an interactive, physics-based snowflake generator as opposed to the typical geometric ones you find everywhere.
  • Exponential growth: I’ll explore how exponential growth appears in Nature and how our perception of these phenomena are inherently limited and potentially dangerous. I’ll not go be going into the typical Malthusian population angle on this.

For all of these I’m hoping to include some interactive simulation or visualization.

If you have a Twitter account, be sure to cast a vote!


2815 = 218 497 496 936 607 064 853 048 583 478 354 175 496 839 440 705 647 678 599 864 575 975 883 972 208 808 167 719 614 290 358 159 090 999 064 327 310 325 620 422 930 884 252 602 183 354 953 346 451 122 776 638 950 446 123 565 515 229 051 718 149 272 758 321 962 318 725 648 740 732 173 736 042 431 692 028 683 588 857 933 856 768 — two hundred eighteen octogintillion, four hundred ninety-seven novemseptuagintillion, four hundred ninety-six octoseptuagintillion, nine hundred thirty-six septenseptuagintillion, six hundred seven sexseptuagintillion, sixty-four quinseptuagintillion, eight hundred fifty-three quattuorseptuagintillion, forty-eight treseptuagintillion, five hundred eighty-three duoseptuagintillion, four hundred seventy-eight unseptuagintillion, three hundred fifty-four septuagintillion, one hundred seventy-five novemsexagintillion, four hundred ninety-six octosexagintillion, eight hundred thirty-nine septensexagintillion, four hundred forty sexsexagintillion, seven hundred five quinsexagintillion, six hundred forty-seven quattuorsexagintillion, six hundred seventy-eight tresexagintillion, five hundred ninety-nine duosexagintillion, eight hundred sixty-four unsexagintillion, five hundred seventy-five sexagintillion, nine hundred seventy-five novemquinquagintillion, eight hundred eighty-three octoquinquagintillion, nine hundred seventy-two septenquinquagintillion, two hundred eight sexquinquagintillion, eight hundred eight quinquinquagintillion, one hundred sixty-seven quattuorquinquagintillion, seven hundred nineteen trequinquagintillion, six hundred fourteen duoquinquagintillion, two hundred ninety unquinquagintillion, three hundred fifty-eight quinquagintillion, one hundred fifty-nine novemquadragintillion, ninety octoquadragintillion, nine hundred ninety-nine septenquadragintillion, sixty-four sexquadragintillion, three hundred twenty-seven quinquadragintillion, three hundred ten quattuorquadragintillion, three hundred twenty-five trequadragintillion, six hundred twenty duoquadragintillion, four hundred twenty-two unquadragintillion, nine hundred thirty quadragintillion, eight hundred eighty-four novemtrigintillion, two hundred fifty-two octotrigintillion, six hundred two septentrigintillion, one hundred eighty-three sextrigintillion, three hundred fifty-four quintrigintillion, nine hundred fifty-three quattuortrigintillion, three hundred forty-six tretrigintillion, four hundred fifty-one duotrigintillion, one hundred twenty-two untrigintillion, seven hundred seventy-six trigintillion, six hundred thirty-eight novemvigintillion, nine hundred fifty octovigintillion, four hundred forty-six septenvigintillion, one hundred twenty-three sexvigintillion, five hundred sixty-five quinvigintillion, five hundred fifteen quattuorvigintillion, two hundred twenty-nine trevigintillion, fifty-one duovigintillion, seven hundred eighteen unvigintillion, one hundred forty-nine vigintillion, two hundred seventy-two novemdecillion, seven hundred fifty-eight octodecillion, three hundred twenty-one septendecillion, nine hundred sixty-two sexdecillion, three hundred eighteen quindecillion, seven hundred twenty-five quattuordecillion, six hundred forty-eight tredecillion, seven hundred forty duodecillion, seven hundred thirty-two undecillion, one hundred seventy-three decillion, seven hundred thirty-six nonillion, forty-two octillion, four hundred thirty-one septillion, six hundred ninety-two sextillion, twenty-eight quintillion, six hundred eighty-three quadrillion, five hundred eighty-eight trillion, eight hundred fifty-seven billion, nine hundred thirty-three million, eight hundred fifty-six thousand, seven hundred sixty-eight (246 digits, 3351 characters)


2814 = 109 248 748 468 303 532 426 524 291 739 177 087 748 419 720 352 823 839 299 932 287 987 941 986 104 404 083 859 807 145 179 079 545 499 532 163 655 162 810 211 465 442 126 301 091 677 476 673 225 561 388 319 475 223 061 782 757 614 525 859 074 636 379 160 981 159 362 824 370 366 086 868 021 215 846 014 341 794 428 966 928 384 — one hundred nine octogintillion, two hundred forty-eight novemseptuagintillion, seven hundred forty-eight octoseptuagintillion, four hundred sixty-eight septenseptuagintillion, three hundred three sexseptuagintillion, five hundred thirty-two quinseptuagintillion, four hundred twenty-six quattuorseptuagintillion, five hundred twenty-four treseptuagintillion, two hundred ninety-one duoseptuagintillion, seven hundred thirty-nine unseptuagintillion, one hundred seventy-seven septuagintillion, eighty-seven novemsexagintillion, seven hundred forty-eight octosexagintillion, four hundred nineteen septensexagintillion, seven hundred twenty sexsexagintillion, three hundred fifty-two quinsexagintillion, eight hundred twenty-three quattuorsexagintillion, eight hundred thirty-nine tresexagintillion, two hundred ninety-nine duosexagintillion, nine hundred thirty-two unsexagintillion, two hundred eighty-seven sexagintillion, nine hundred eighty-seven novemquinquagintillion, nine hundred forty-one octoquinquagintillion, nine hundred eighty-six septenquinquagintillion, one hundred four sexquinquagintillion, four hundred four quinquinquagintillion, eighty-three quattuorquinquagintillion, eight hundred fifty-nine trequinquagintillion, eight hundred seven duoquinquagintillion, one hundred forty-five unquinquagintillion, one hundred seventy-nine quinquagintillion, seventy-nine novemquadragintillion, five hundred forty-five octoquadragintillion, four hundred ninety-nine septenquadragintillion, five hundred thirty-two sexquadragintillion, one hundred sixty-three quinquadragintillion, six hundred fifty-five quattuorquadragintillion, one hundred sixty-two trequadragintillion, eight hundred ten duoquadragintillion, two hundred eleven unquadragintillion, four hundred sixty-five quadragintillion, four hundred forty-two novemtrigintillion, one hundred twenty-six octotrigintillion, three hundred one septentrigintillion, ninety-one sextrigintillion, six hundred seventy-seven quintrigintillion, four hundred seventy-six quattuortrigintillion, six hundred seventy-three tretrigintillion, two hundred twenty-five duotrigintillion, five hundred sixty-one untrigintillion, three hundred eighty-eight trigintillion, three hundred nineteen novemvigintillion, four hundred seventy-five octovigintillion, two hundred twenty-three septenvigintillion, sixty-one sexvigintillion, seven hundred eighty-two quinvigintillion, seven hundred fifty-seven quattuorvigintillion, six hundred fourteen trevigintillion, five hundred twenty-five duovigintillion, eight hundred fifty-nine unvigintillion, seventy-four vigintillion, six hundred thirty-six novemdecillion, three hundred seventy-nine octodecillion, one hundred sixty septendecillion, nine hundred eighty-one sexdecillion, one hundred fifty-nine quindecillion, three hundred sixty-two quattuordecillion, eight hundred twenty-four tredecillion, three hundred seventy duodecillion, three hundred sixty-six undecillion, eighty-six decillion, eight hundred sixty-eight nonillion, twenty-one octillion, two hundred fifteen septillion, eight hundred forty-six sextillion, fourteen quintillion, three hundred forty-one quadrillion, seven hundred ninety-four trillion, four hundred twenty-eight billion, nine hundred sixty-six million, nine hundred twenty-eight thousand, three hundred eighty-four (246 digits, 3331 characters)

You should always order the bigger pizza. While an 8“ pizza is roughly 50 square inches, a 16” pizza is 200 square inches, which is 4 times bigger but most pizza places charge by radius and don’t consider the overall area of the pizza. An NPR study found that one 20” pizza is actually bigger than two 14” pizzas, but is also, on average, $9.00 cheaper. Source