Interesting Math Theories

[Alolan_Apples]

I'm now at the 75-entry mark. So another chapter has closed. You can figure out what today's entry is going to be. Since it's the fifth entry, and an odd-numbered entry, it's going to be another fact blog entry. Like what I talked about on my 60th blog entry (the one about politics), I mentioned that I'm going to have a math blog. And this entry is all about that. Math theories that are true and heard of before, but never learned in under-college schools.

• If you add a linear term to a sine or cosine function (the trigonometric functions that look like waves), it creates a trend line for the linear function that the waves follow.
• If you multiply or divide the independent variable outside the sine or cosine function, then the amplitude changes as it moves away from the center. It only increases if you multiply, but decreases if you divide.
• If you raise the variable inside the sine or cosine function to a power greater than 0, then the frequency changes as it moves away from the center. If the exponent is greater than 1, the waves are closer to each other away from the center. If it's less than 1, they move further apart from each other.
• In a parametric function, if the function of T is the same for both X and Y, then the actual Cartesian function looks like a linear equation with a slope of 1 and y-intercept of 0.
• A prime polynomial is a polynomial where all the roots are irrational or imaginary. Basically speaking, they cannot be broken down to smaller polynomials. For example, a prime trinomial can't be factored into two smaller binomials, as the discriminant in the quadratic equation is either negative or not a perfect square.
• If the quadratic equation you're solving is a perfect square trinomial, then the discriminant is always 0. Differences of squares quadratic equations are better off if you solve them using the square roots method.
• The size of the outer radius in relationship to the inner radius of a torus determines the thickness of the ring. If the outer radius is greater than the inner radius, then the ring gets thinner as the outer radius is getting bigger.
• The Pythagorean Theorem can be used to determine the triangle type too. If a2+b2<c2, then the triangle is obtuse. If a2+b2=c2, then it's a right triangle. If a2+b2>c2, then it's acute.
• Multiplying two terms with either the same exponent or same base can be combined. If they have the same base, but different exponent, the exponents can be added. If they have a different base, but same exponent, then the bases can be multiplied while the exponent is left alone.
• The quickest way to count how many factors a number has is through prime factorization. Once the number is in prime factorization, you can strip off the exponents, add one to each, and multiply all the sums. If a number doesn't have an exponent, then the exponent is 1.

There are more interesting theories, but 10 is good enough. If you read this blog entry, you have learned something new.

 

[NewLeaf13]

Whoa, your really smart to know all that.