Facts about the numbers (and the functions)

While I already had two fact entries, this one is more of a true fact entry. The purpose of these entries is to share some amazing facts of the world. I am still not far from the math entries yet. I am going over three different types of facts, the facts about all 10 numbers to each digit, other numerical facts, and some interesting math theories.

Digital Facts

All ten numbers that can be in a digit have some amazing facts about them. It doesn’t matter which one is which, they all have something amazing.

  1. 1 is the only natural number to be neither prime nor composite.
  2. 2 and 5 are the only prime numbers to end with a 2 or a 5.
  3. 3 is the last one’s digit number to be part of a composite number.
  4. 4 is the smallest composite number. Also, it’s the only number to have the same amount of letters in its name as the value in the English language.
  5. 5 is the only odd number to never be prime in numbers with two or more digits.
  6. 6 is the smallest number to have a composite amount of factors.
  7. There are 7 days in the week.
  8. No perfect square ends with a 2, 3, 7, or 8.
  9. 9 is the only odd composite number smaller than 10.
  10. All products ending with a 1, 5, 6, and 0 will always have the same ones digit if both factors multiplied have the same ones digit.

Other Number Facts

  • The sum of the first 10 numbers is 55. The average is the same as the median, which is 5.5.
  • The product of the first 10 numbers is 3,628,800. You can find the product by using factorials (!) too.
  • The least common multiple of the first 10 numbers is 2,520.
  • The palindrome of 89 and 98 uses the most iterations out of all numbers under 10,000. 196 doesn’t have a palindrome as of now.
  • 64 is the smallest number besides 1 that can be both a square and a cube.
  • The perimeter and area of a square is the same number if the side length is 4.
  • The surface area and volume of a cube is the same number if the edge length is 6.
  • 1,000 is the first number to have an “a” in its word name.
  • All numbers from 1 to 10 have 3, 4, or 5 letters in their names.
  • 7 is the smallest multisyllabic number greater than 0. 12 is the largest number to have only one syllable.

Interesting Math Facts

  • The sum of a trigonometric function (take sine for example) and a linear term (either positive or negative) deflects the cycle and creates a trend line that resembles the linear function.
  • Multiplying to or dividing x from a sine or cosine function on the outside causes the amplitude to change as the wave diverges from the center. Multiplication makes the amplitude greater as it moves away as division decreases it.
  • Exponents and roots of the term inside a trigonometric function alters the wavelength as the wave diverges from the center. Exponents increase the frequency away from the center, roots do the same thing, but only decreases.
  • Adding a number ending with a 1 increases the ones digit by 1 every time, then moves from 9 to 0 at the end. Adding a number ending with a 9 does the opposite to the ones digit, but still makes the overall number bigger.
  • Adding a number ending with a 2 makes the ones digit go in this pattern: 1, 3, 5, 7, and 9 for the odds, and 2, 4, 6, 8, and 0 for the evens. Adding a number ending with an 8 makes it go backwards.
  • Adding a number ending with a 3 makes the ones digit go in this pattern: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0. Adding a number ending with a 7 (or going to the next date on the same day of the week) makes the ones digit go the other way.
  • Adding a number ending with a 4 makes the ones digit go in this pattern: 1, 5, 9, 3, and 7 for the odds, and 4, 8, 2, 6, and 0 for the evens. Adding a number ending with a 6 makes it go backwards.
  • Adding a number ending with a 5 makes the ones digit alternate between two different numbers. 1 and 6, 2 and 7, 3 and 8, 4 and 9, and 5 and 0. Adding a number ending with a 0 yields a constant result.
  • Multiplying two numbers with the same base and different exponent will keep the base the same, but the exponents add up. Multiplying two numbers with a different base, but same exponent will keep the exponent the same, but the bases multiply.
  • The discriminant in the quadratic formula will always be 0 when plugging in a perfect square trinomial in the quadratic formula.
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