Posts Tagged ‘side’
Friday, September 25th, 2009
Four-Color Theorem Explained
Description
A detailed tutorial on the four-color theorem. Step by step tutorial including several examples of the four-color theorem for reference.
Overview
The four-color theorem is a concept in math that states that given any seperation of a plane into seperate regions, the regions can be colored in using at the most four colors so that no two adjacent regions have the same color. These planes are called maps, and in fact a real map is an example of one. In order for two regions to be adjacent, they must share a side. If they share a point they are not considered adjacent.
Tags: adjacent, color, four, four color map theorem, four-color, four-color theorem, Geometry, map, Math, planes, point, regions, seperate, side, theorem
Posted in Geometry | No Comments »
Thursday, September 17th, 2009
An Introduction to the Law of Cosines
Description
A detailed tutorial on the Law of Cosines and proving the Law of Cosines. Step by step tutorial including several examples of proving the Law of Cosines for reference.
Overview
The Law of Cosines is a formula that is used to relate the sides of a triangle to the cosine of one of its angles. The Law of Cosines can be expressed as:
Where a, b, and c are the sides of the triangle. If the triangle is a right triangle then this simplifies to the Pythagorean Theorem.
Tags: angle, cosine, cosine formula, cosine rule, law of cosines, Math, pythagorean theorem, side, triangle, trigonometry
Posted in Trigonometry | No Comments »
Thursday, September 17th, 2009
An Introduction to the Law of Sines
Description
A detailed tutorial on the the Law of Sines and how to prove the Law of Sines. Step by step tutorial including several examples of how to solve problems with the Law of Sines for reference.
Overview
The Law of Sines is a formula that can be used when a triangle has both side and angle measures. The Law of Sines is expressed as:
Where a, b, and c represent the sides, and A, B, and C represent the angles that are opposite of those sides. This formula looks very similar to the Pythagorean Theorem.
Tags: angle, law of sines, Math, side, sine, sine formula, sine rule, sines law, triangle, trigonometry
Posted in Trigonometry | No Comments »
Tuesday, September 15th, 2009
An Overview of the Different Types of Triangles
Description
A detailed tutorial on the different types of triangles. Step by step tutorial including several examples of the different types of triangles for reference. Knowledge of the different types of triangles is required for all geometry classes.
Overview
Everyone knows what a triangle is, but a triangle is more than just “a triangle” – it could be one of several different types of triangles. Different types of triangles are identified by the different traits of their sides and their angles. The types are as follows:
Scalene Triangles: All sides and all angles are of different measures and lengths.
Right Triangles: One angle of the triangle is 90 degrees.
Isosceles Triangles: 2 sides and 2 angles have the same measures and lengths.
Equilateral Triangles: All side lengths are the same and all angles are 60 degrees.
Equiangular Triangles: All angles measure 60 degrees but all sides could have different lengths.
Tags: 60, 90, angle, degrees, equal, equiangular, equilateral, Geometry, isosceles, length, Math, measure, right, scalene, side, triangle
Posted in Geometry | No Comments »
Friday, September 11th, 2009
How to Use SOHCAHTOA
Description
A detailed tutorial on the solving of SOHCAHTOA. Step by step tutorial including several examples of how to solve SOHCAHTOA problems for reference.
Overview
SOHCAHTOA, often spaced out to spell SOH-CAH-TOA, stands for Sine = Opposite/Hypontenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. You use it with an angle to help solve for the sine, cosine, or tangent of that angle. What Opposite, Adjacent, and Hyptonuse stand for are the sides of a triangle – the side exactly opposite your angle, the hypotenuse, and the third non-hypotenuse side that is next to your angle. Because of this, SOHCAHTOA can only be used with a right triangle. The values for opposite, adjacent, and hypotenuse are the length of the side of the triangle it stands for. It is not necessary to know the measure of the angle before using SOHCAHTOA.
Tags: adjacent, angle, cosine, Geometry, hypotenuse, length, Math, opposite, right triangle, side, sine, SOH-CAH-TOA, SOHCAHTOA, tangent, triangle, trigonometry
Posted in Geometry, Trigonometry | No Comments »
Tuesday, September 8th, 2009
How to Find the Volume of a Cube
Description
This is just a short video showing a visual display of the volue of a small cube, and a formula for that specific cube is expressed at the end. That formula can be used to derive the formulas for other cubes.
Overview
A cube is a common object – they are any 3D square object with sides all measuring equal length. This can expressed the same way as a cube, but is easier to solve.
V = l * w * h = s^3
The length, width, and height are all the same on a cube so you can simply “cube” the number, or put it the third power. This is also why we call putting things to the third power “cubing”.
Tags: area, cube, cubes, finding volume, Geometry, height, length, Math, side, square, volume, volume of a cube, width
Posted in Geometry | No Comments »
