Factorial numbers. The factorial is the product of all the numbers from 1 through N. Factorials are frequently used in the field of Combinatorics to calculate permuations and combinations.
Fibonacci numbers. A Fibonacci number is the sum of the previous two Fibonacci numbers. The first Fibonacci number is 0 and the second Fibonacci number is 1. Starting with these, we can compute any other Fibonacci number. This number appears a lot in nature, especially in the way plants grow.
Prime numbers. A prime number is a number that is divisible only by itself and 1.
Computing Pi. You can compute PI in many different ways. This page computes PI by generating random point coordinates. The area of the circle vs. the area of the square has a relationship defined by PI.
Prime factors. The prime factors of a number form a unique list of prime numbers whose product is the original number.
GCD. The Greatest Common Divisor of any two numbers A and B is the largest number that divides evenly into both numbers. It is useful for reducing fractions to the simplest terms.
LCM. The Least Common Multiple of any two numbers A and B is the smallest number that is evenly divisible by both A and B. It is used as the lowest common denominator when adding or subtracting fractions. It is used for calculating the rotations of gears. Similarly, it is used for determining planetary alignments. The LCM is easy to compute from the GCD.
Pythagorean Theorem. The Pythagorean Theorem describes the relationships between the lengths of the sides of a right triangle.
Multiplication Table. Draw a multiplication table in any size you choose.
This is an example of a Single Page Application (SPA) like we might do in the GDS 089B course. Each screen serves its specific purpose. The screens are distinguished by hashes in the URL. When the hash changes, the screen change. We call them screens because they are not actually separate pages, they are all on one page.
The factorial is the product of all the numbers from 1 through N. Factorials are frequently used in Combinatorics to calculate permuations and combinations.
Note: Factorials of numbers greater than 18 may not be accurate.
The first few factorial numbers are:
A Fibonacci number is the sum of the previous two Fibonacci numbers. The first Fibonacci number is 0 and the second Fibonacci number is 1. Starting with these, we can compute any other Fibonacci number. This number appears a lot in nature, especially in the way plants grow.
Note: Numbers greater than Fibonaci(75) may not be accurate.
The first few Fibonacci numbers are:
A prime number is a number that is divisible only by itself and 1.
The first few prime numbers are:
The Greatest Common Divisor of any two numbers A and B is the largest number that divides evenly into both numbers. It is useful for reducing fractions to the simplest terms.
The Least Common Multiple of any two numbers A and B is the smallest number that is evenly divisible by both A and B. It is used as the lowest common denominator when adding or subtracting fractions. It is used for calculating the rotations of gears. Similarly, it is used for determining planetary alignments. The LCM is easy to compute from the GCD:
lcm(a,b) = |ab| / gcd(a,b)
The prime factors of a number form a unique list of prime numbers whose product is the original number.
The Pythagorean Theorem describes the relationships between the lengths of the sides of a right triangle. In the following equation, c is the hypotenuse.
a2 + b2 = c2
Enter any two of the sides to compute the third side.
You can compute PI by generating random point coordinates. The area of the circle is π r2. If r=1, then the area of the circle is π and the area of the square is 4. Therefore, the ratio of the number of points inside the circle to the number inside the square is π / 4.
The actual value of PI is 3.141592653589793. You can get closer to the actual value of PI by generating more points, but it takes more time. This is a relatively slow way of calculating PI. There are other much faster ways to compute PI.
Note: it takes only a short time to do the calculations, but it takes a while to draw the image.
You can calculate the number of ways of choosing k items from a set of n items. This is called C(n,k) but it is more commonly notated like this:
(nk)
The calculation for C(n,k) uses the Factorial function. It is easily calculated like this:
n!
C(n,k) = ––––––––
k! (n–k)!
The combination function can also be used to form Pascal's Triangle, where every number is the sum of the two numbers above it. These numbers are also used as coefficients in the Binomal Theorem.
A quadratic equation is the description of a parabola. A parabola may cross the x axis in one place, in two places, or not at all. The Quadratic Equation tells you the y coordinates where the parabola crosses the x axis.
Quadratic Equation has the form:
y = ax2 + bx + c
Solution has the form:
– b ± √ b2 – 4ac
x = –––––––––––––––––
2a
If the value under the square root sign (called the discriminant) is positive, the result will be two real numbers. (Try 1, 5, 4.)
If the value under the square root sign is negative, the result will be two complex numbers (with a real and an imaginary component). (Try 2, 4, 4.)
If the value under the square root sign is zero, the result will be only one real number solution. (Try 1, 4, 4.)
Enter the coefficients here:
Results will go here: