I'm scheduling all my posts here for midnight EST btw :3
Math Fact #14: A Klein bottle is an example of a 3D shape without a volume. This means that if you were to trace a line from one point of a Klein bottle and go all the way around, the line will be flipped upside down and eventually return to the starting point.
Math Fact #13: The Goldbach Conjecture shows that any even number greater than two can be expressed as a sum of two primes. For instance... 4 = 2 + 2 8 = 3 + 5 16 = 13 + 3 26 = 19 + 7
OMG I'M SO SORRY I FORGOT YESTERDAY'S MATH FACT I'LL RELEASE YESTERDAY'S, TODAY'S, AND TOMORROW'S MATH FACTS AT THE SAME TIME
Math Fact #11: Square roots can be expressed as a power of ½. Similarly, cube roots can be expressed as a power of ⅓. For any root (nth root), it can always be expressed as a power of 1/n. This is helpful when trying to find the derivative of a function.
Math (and Physics) Fact #10: If you push a cube with a mass of 10^(2n + 1) (where n is a whole number) into a cube with a mass of 1 on a frictionless plane, the amount of collisions within the simulation is equal to the digits of π.
Math Fact #9: (sugg. @grggrulz) There is algebraic proof that 0.99999... = 1. Any number subtracted from itself is 0. And 1 - 0.99999... = 0.00000... Because the amount of 9s you can put at the end is endless, there will always be a 0 you can put on the end. Thus, 0.999... = 1
Math Fact #8: (sugg. @grggrulz) The expression (a + b)ⁿ can be expanded using Pascal's triangle. Pascal's triangle is a triangle where every cell is the sum of the two cells above it. It also happens that the n - 1st row is the coefficients of the expansion of (a + b)ⁿ.
Math Fact #7: There exists something known as the Collatz conjecture. Start at any number, n. If n is odd, apply the rule 3n + 1. If n is even, apply the rule n ÷ 2. Now repeat for every instance of n. Eventually, you will reach the same 4, 2, 1 loop.
Math Fact #6: The Hz for a musical note actually has a formula. This formula can be modified to account for different master tunings (A = 440 Hz) and different EDOs (12 EDO). t represents master tuning n represents note of the octave e represents EDO
Math (and Physics) Fact #5: In terms of light physics, the normal of the point on a surface that a ray is hitting is the exact same as the tangent line of the equation of the surface on the same point.
Math Fact #3: Infinity comes in different sizes. We can measure these infinites in cardinality, which is the amount of elements in a list. Aleph zero (ℵ₀) is the cardinality of all natural numbers, whereas the cardinality of all real numbers is 2^ℵ₀, or Aleph one (ℵ₁).
Math Fact #1: An interesting way of looking at why 1/0 = undefined is the following image. You can clearly see that by solving for x in 1/x = 0, it ends up with the equation 1 = 0, which is false, even though all the algebra was correct.
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