In 1929 in Göttingen, a challenge to express any whole number using the number 2 precisely four times, and using only well-known mathematical symbols, was introduced.
The first few numbers are easy:
1 = (2 + 2)/(2 + 2),
2 = (2/2) + (2/2),
3 = (2 x 2) - (2/2),
4 = 2 + 2 + 2 - 2.
The game became much more difficult even for Göttingen’s finest mathematical minds. Hundreds of hours were spent playing the game with higher and higher numbers - until Paul Dirac found a simple and general formula enabling any number to be expressed using four 2s, entirely within the rules. He had rendered the game pointless.
Dirac’s solution relies on a basic property of logarithms:
where the number of radicals is exactly n square roots.
One may think that Dirac killed the game using only three 2s. Each symbol in the formula is very common in mathematics, so Dirac’s solution is still within the rules of the game.
Content inspired by The Strangest Man by Graham Farmelo
Honestly, most people don’t study for a math test. Mostly because there’s almost no actual information to study for. And there’s no way you’re going to give yourself any extra work by giving yourself more problems right? Well I myself am not really an all-night study person (yet) and I will share how I study and other methods of studying for a high school math test.
1. NOTES: (Most common) Listen, I take notes for in-class purposes but I don’t really use them otherwise. Some people worship their notes. It really just depends on how you learn. If your notes are full of helpful tips and examples, then definitely read over those. 2. ASKING: Don’t ever be afraid to ask a teacher for help on a certain problem. They’re there to teach you obviously. Even if you’re socially awkward like me, you can still ask them. It’s preferred to ask a teacher sometime before or after class. 3. PROBLEMS: Although it may come off as extra work, this CAN help you, especially if it’s the night before the test. Find some problems in the book and try to work them out. You don’t necessarily have to take out paper and work them all out if you don’t want to. You can simply just think about how to solve the particular type of problem. 4. SKIMMING: (My personal way of studying) Open your textbook and flip through the chapter you are currently studying in class. Skim the information and take note of any key concepts or examples. Look and see how each example is worked out and why. You can also skim your homework to see how problems were solved earlier. 5. FLASHCARDS: This really depends on the type of class you’re taking and how you learn. If you’re a more English/Foreign Language oriented learner, this could help. Make some flashcards on chapter vocab and formulas and study them. 6. GROUPS: Why not make math fun (If not already)? Do some problems with friends and you can definitely stick in some information into your brain. Friends can also help you with problems if a teacher is unavailable.
You CAN study for a math test, believe it or not. Remember to ask questions if you’re confused so you can pass that test!
Riddles Intellectual silliness (epithet of the INTP) Loud neutrality in arguments Nonverbal indications of boredom Math Telling you how smart they are Telling you how smart they think you are based on how much less dumber you are than they are than other people are Being overly complex
Y/N:“I think I almost get it. Maybe I need another example.”
N:“It’s actually very simple. For example there may be a lot of smart, cute girls, beautiful girls, girls with a good personality but it’s very rare that all these are combined in a girl. That’s why I’m very lucky to know you because the chances are zero for me to meet another girl like you.”
guys i know we all know that pidge is amazingly smart with science and math…..but do you think she likes english??? do you think she likes writing. what if she does, like what if she loves creative writing bc she has so many ideas and writing allows her to get them all out in a different way