In this article, we explore the ubiquitous Fibonacci sequence and its presence in nature and in many aspects of our life.

### What Are Fibonacci Numbers?

A guide to solving for centroids and centers of gravity of different compound shapes using the method of geometric decomposition. Learn how to obtain the centroid from different examples provided.

### Calculating the Centroid of Compound Shapes Using the Method of Geometric Decomposition

The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if you wanted to work out the...

### The Density, Mass and Volume Magic Triangle: How to Calculate Density of a Solid Shape

This guide shows you the math behind working out a bolt circle diameter (BCD) or pitch circle diameter (PCD) and gives tables you can use in your calculations.

### How to Calculate Bolt Circle Diameter (BCD)

Solving problems related to plane geometry especially polygons can be easily solved using a calculator. Here is a comprehensive set of problems about polygons solved using calculators.

### Calculator Techniques for Polygons in Plane Geometry

A composite shape or compound shape is a shape that is made from other shapes such as two rectangles (L-shape) or a triangle and a rectangle. If you are going to calculate the area of a composite shape then you need to break up composite shape into...

### How To Calculate The Area Of A Composite Or Compound Shape (rectangles, triangles, circles).

The article is written in rather technical level, providing an overview of linear regression. Linear regression is based on the ordinary list squares technique, which is one possible approach to the statistical analysis. Both univariate and multivariate linear regression are illustrated on small concrete examples. In addition to the explanation of basic terms like explanatory and dependent variables, we will see how to interpret results obtained by a regression analysis.

### Univariate and Multivariate Linear Regression

The marginal rate of technical substitution of Labor (L) for Capital (K) is the slope of an isoquant multiplied by -1. Since the slope of an isoquant is moving down, the isoquant is given by –ΔK/ΔL...

### Marginal Rate of Technical Substitution

Area and perimeter can be difficult to work out if you can't remember which one is which. Here is a great hub to help you remember and also help you work out more complicated maths in compound shapes.

### Math Help: What Are Area and Perimeter? How to Work out the Area and Perimeter of a Compound Shape

When solving complex arithmetic expressions, the order in which you perform which functions is crucial in getting the correct answer. The acronym PEMA is a good mnemonic tool for these problems.

### How to Use PEMA to Guide Order of Operations in Arithmetic Problems

In this article I want to use a specific polynomial equation to introduce the Whittaker method for finding the root that has the smallest absolute value.

### Whittaker Formula and the Fibonacci Numbers

Percentile refers to the position of a piece of data in a distribution, while percent refers to rate per 100.

### What Is Percentile Rank? How Is It Different From Percentage?

A basic discussion on the null hypothesis, z-scores, and probability. This article includes examples of the null hypothesis, one-tailed, and two-tailed tests. A coin is tossed and comes up tails ten times: is this just random chance, or is an unfair coin being used? Learn when to reject the null hypothesis: if the probability (P) is less than the chosen significance level, the null must be rejected.

### Null Hypothesis and Formulas: A Definition With Examples

Understanding percentages and learning how to calculate them is a fundamental skills of mathematics. This articles describes how to calculate a variety of types of percentages that are used in our world each and every day.

### How to Calculate Percentages

Find out how to perform AC test in determining if a trinomial is factorable. Once proven factorable, proceed with finding the factors of the trinomial using a 2 x 2 grid.

### Factoring Quadratic Trinomials Using the AC Test

Not everybody knows why a plus b whole square is i.e. (a+b) 2 = a2+b2+2ab and why exactly it has been generalized.So, here I come up with the geometrical proof that shows up the results.

### Why (a+b) 2 = a2+b2+2ab ?

Solving problems related to plane geometry especially circles and triangles can be easily solved using a calculator. Here is a comprehensive set of calculator techniques for circles and triangles in plane geometry.

### Calculator Techniques for Circles and Triangles in Plane Geometry

This Hub shows how to analyze data obtained from a statistical survey. The methods prescribed in this Hub are basic, yet effective.

### How to Analyze a Statistical Survey: Standard Deviation, Outliers, and More

Follow these instructions below to develop a truncated cone. A truncated cone is a conical shape which has had it's top cut off at an angle. Sometimes you might need to develop these truncated cones as duct elements. Developing a truncated cone can...

### How to Develop a Truncated Cone

Need help with math? Get math help online with the Math Made Easy! series of geometry tutorials, including surface area of a cylinder.

### Math Made Easy! How to Find the Surface Area of a Cylinder

How to learn your times tables fast. There are a few tricks to help you with your times tables and even a link to my video "How to Learn Your Times Tables Fast"

### How to Learn Times Tables

Game Theory is one of the most fascinating branches of mathematics with tons of applications to fields ranging from the social sciences to the biological sciences. In this article, we will look at some basic examples of game theory and its application to real-world situations.

### What Is Game Theory? A Basic Introduction and Example

This geometry tutorial shows how to find the area of a circle. Included are math tips and easy to follow problems and answers for finding the area of a circle.

### Math Made Easy! How to Find the Area of a Circle

Finding the mean, median, and mode of a data set is an important first step in learning and implementing basic statistical techniques. This hub will teach you how to calculate these measures.

### Measures of Central Tendency: Mean, Median, and Mode

Here you will be shown to work out the area and perimeter of a C shape. A C shape is a compound shape made up of 3 rectangles. Make sure you know how to find the area and perimeter of an L shape before you attempt this lesson on C shapes. To work...

### Compound C Shapes: How to Calculate the Perimeter and Area of a C Shape.

How many cats fit into the trunk of a Honda Civic....and other fun math problems involving our favorite feline friends

### Cat Mathematics: How Many Cats Fit Into the Trunk of a Honda Civic...

How to develop a cone or how to create a flat pattern of a cone can be achieved in a few easy geometrical steps. The geometrical method shown below does however have inaccuracy, so at the end of this hub I have included a mathematical formula to...

### How to Develop a Cone - Cone Development

Need high school geometry homework help? This Math Made Easy! Geometry Tutorial explains how to find the circumference of a circle with easy to follow problems and solutions.

### Math Made Easy—How to Find the Circumference of a Circle

How to convert a hexadecimal to a decimal and a decimal to a hexadecimal without using any calculators or special knowledge.

### How to Convert Hexadecimal to Decimal and Decimal to Hexadecimal Manually

The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of its faces.

### How to Find the Surface Area of Right-Angled and Isosceles Triangular Prisms

Zenos Paradox has been around since before Christ and has baffled many people. An explanation and debunking of the paradox; why it is no paradox at all but a simple mathematical description of what we see happening all around us.

### Understanding and Solving Zeno's Paradox

This is an action research proposal which seeks to address the failure of some students to solve and analyze mathematics word problems due to poor reading comprehension.

### Action Research Proposal: Mathematics Problem-Solving Skill and Reading Comprehension

Card game problems are a recurring theme in probability. In fact, a small set of basic principles allows you to crack game problems with ease, including the notorious poker hand problems.

### Cracking Probability and Combinatorics: Card Game Problems

This guide explains everything you need to know about circles, including calculation of area, segment area, sector area, length of an arc, radians, sine and cosine.

### How to Calculate Arc Length of a Circle Segment and Sector Area

Stuck on long division of polynomials? Here's an easy, step-by-step guide to "synthetic division" to help you with tricky Algebra homework.

### Math Help: How to Do Long Division of Polynomials Easily (Synthetic Division)

The mean average from an ungrouped frequency table can be found by following these three simple steps: Step 1. First you will need to add a new column onto the end of the frequency table. You can label this column fx as you are going to multiply...

### How to Get the Mean Average From a Frequency Table

Keeping our calendar in sync with solar time requires more than just adding a day every four years. We need to add a second once in a while, known as a leap second. We also need to skip some leap years.

### The Algorithmic-Rule for Leap Years and Leap Seconds

A quick way to divide by 0.5 or ½ is to double the number (or multiply number by 2). The reason for this is because two halves go into a whole.

### Dividing by 0.5: A Simple Method to Divide by a Half

A hands-on math activity for middle schoolers. The topic being taught here is circumference and area of circles and the hands-on activity is using two different types of baked pies.

### Circumference and Area of a Circle: A Middle School Math Hands-On Lesson

Here you will be shown how to simplify expressions involving brackets and powers. The general rule is: (xm)n = xmn So basically all you need to do is multiply the powers. This may also be called the exponent bracket rule or indices bracket rule...

### Powers in Brackets: How to Use the Bracket Power Rule

Need help with trig homework or a review of the basics? This article explains in plain English how to visualize the unit circle as just a set of triangles, how a sine and cosine work, and radians.

### Trigonometry: The Unit Circle [in Plain English]

How do you learn to calculate percentages in your head? Practice, practice, practice. Seriously, doing mental math in your head isn't that hard when you understand a few shortcuts. Here's our tips.

### How Much Is Seventy Percent Off? (Calculating Percentages in Your Head)

If you are asked to work out the product of two numbers then you need to multiply the two numbers together. If you are asked to find the sum of two numbers then you need to add the numbers together.

### Math Help—How to Work out the Product and Sum of Two Numbers

Working out the odds of an event occurring allows us to estimate the number of times that event will take place in future trials. Permutations/combinations are also an important part of the analysis.

### How to Work Out Odds, Permutations and Combinations and Calculate the Probability of an Event

The special theory of relativity is a theory by Albert Einstein, which can be based on the two postulates Postulate 1: The laws of physics are the same (invariant) for all inertial (non-accelerating) observers.* Postulate 2: In a vacuum the speed...

### Minkowski Diagram

Though we all know how to use the Pythagorean Theorem, few know of the many proofs that accompany this theorem. Many of them have ancient and surprising origins.

### Early Proofs of the Pythagorean Theorem by Leonardo Da Vinci, Ptolemy, Thabit ibn Qurra, and Garfield

One of the best tools for statistical analysis is Microsoft Excel. In this article, I will cover how to find relative distribution in a list of data using the COUNTIF() function.

### Using Excel COUNTIF Function in Frequency Distribution

Do you have problems converting between cups, pints, quarts, and gallons? Many people do. Learn a method of conversion that will help you to remember the units and will give you a visual way to go about converting between units. This method is useful for children and adults.

### How to Remember Customary System Measurement Conversions: Cups, Pints, Quarts, Gallons

There is no biggest number, but really, how much is a thousand, a million, a googolplex or even a googolplexian? This look into big numbers may give you an idea how big they are.

### Taking a Perspective Look Into Big Numbers

Regression equations are frequently used by scientists, engineers, and other professionals to predict a result given an input. These equations have many applications and can be developed with relative ease. In this article I show you how easy it is to create a simple linear regression equation from a small set of data.

### How to Create Your Own Simple Linear Regression Equation

Al-Biruni a pioneering Muslim scientist figured out a truly remarkable and ingenious method to calculate the radius of the earth (and subsequently its circumference etc.). This was very simple yet accurate requiring just four measurements in all to...

### Al-Biruni's Classic Experiment: How to Calculate the Radius of the Earth

This guide teaches you how to solve the surface area and volume of different polyhedrons such as prisms, pyramids. There are examples to show you how to solve these problems step-by-step.

### How to Solve for the Surface Area and Volume of Prisms and Pyramids

A simple, step by step guide about how to find the Pearson's correlation coefficient, r, and how to calculate the coefficient of determination on your TI-89 calculator.

### How to Find the Correlation Coefficient on a TI-89 Calculator

This is a full guide in finding the general term of sequences. There are examples provided to show you the step-by-step procedure in finding the general term of a sequence.

### How to Find the General Term of Sequences

If you are asked to translate a shape then you need to move the shape to a new position on the coordinate grid. Usually, the directions of the translation are given in terms of a vector. The vector contains 2 numbers which are written vertically...

### How to translate a shape on a coordinate grid using a vector. Math help.

Trig graphs are easy once you get the hang of them. Once you learn the basic shapes, you shouldn't have much difficulty. The main problems A-Level students have, in my experience, are: Remembering which is y = sin x and which is y = cos x....

### Trigonometry—Graphing the Sine, Cosine and Tangent Functions

Don't let mind readers and magicians mess with your mind with number tricks. Learn their secrets and beat them at their own game.

### It's Not Magic, It's Mathematics

If the angles in a triangle are given as algebra (usually in terms of x), and you are asked to find out the size of each angle, then you can follow these 3 simple steps to find all of the angles. Step 1 Add up the 3 angles that are given and...

### How to Work Out the Angles in a Triangle When the Angles Are in Algebra.

How to do Standard Deviation manually in six straightforward steps, includes a step by step of how to do this using Excel, with screenshots and a link to a sample Excel sheet.

### How to Calculate Standard Deviation

To work out a fraction of a number all you need to do is divide the number by the denominator of the fraction and multiply this answer by the numerator. Example 1 Work out 3/8 of 48. First of all divide 48 by the denominator: 48 ÷ 8 =...

### Math Help: How to Work Out a Fraction of a Number

The grid method is a great fool proof method to help you with multiplication. As long as you follow these simple steps and have good knowledge of place value and your timetables this is a great method

### Math Help: How Do You Multiply Using the Grid Method? Partition the Units, Tens and Hundreds to Make It Simplier

Defines polynomials by showing the elements that make up a polynomial and rules regarding what's NOT considered a polynomial. Learn about different types, how to find the degree, and take a quiz to test your knowledge.

### What is a Polynomial?

A compound H-shape is made up of 3 rectangles. Make sure you can work out the area of an L-shape first before you attempt this one. If you are finding the area of a compound H-shape all you need to do is split the H-shape up into 3 rectangles and...

### Calculating the Area of Compound H Shapes

Roman numerals have been around for about 3,000 years, and they became a recognized number system that was used around the world.

### How To Understand Roman Numerals

The graph and location of a parabola depend on its equation. This is a step-by-step guide in graphing different forms of a parabola in the Cartesian coordinate system.

### Graphing a Parabola in a Cartesian Coordinate System

This article shows you how to multiply fractions in four easy steps. How do you multiply mixed numbers? What is an improper fraction? This article, which includes a short video, will answer all these questions and leave you with the knowledge and confidence to multiply any fractions.

### How to Multiply Fractions in Four Easy Steps

Finding the nth term of a decreasing linear sequence can by harder to do than increasing sequences, as you have to be confident with your negative numbers. A decreasing linear sequence is a sequence that goes down by the same amount each time....

### Finding the nth term of decreasing linear sequences (math help)

Speed, distance and time can be calculated using a magic triangle. D (the distance) goes in the top of the triangle, S (speed) goes in the bottom left of the triangle and T (time) goes in the bottom right of the triangle. If you want to calculate...

### Using the Magic Triangle for Speed, Distance and Time (Compound Measures)

Pythagoras and trigonometry (basic) both work in right angled triangles. In this hub you will be shown how to choose the correct one. Pythagoras is used when you have a right angled triangle and you need to work out one of the missing side...

### Pythagoras vs. Trigonometry—How to Know When to Use Trig or Pythag in Your Math Exams

Once I was preparing to take a difficult standardized test, which evaluates math and logic skills for university entrance. It was an online exam with a timer and I had to make calculations without using a calculator. Techniques of fast mental math discussed here became a true godsend for me!

### How to Calculate Quickly Without a Calculator

A quadrant is a quarter of a circle. So to work out the area of a quadrant, first work out the area of the whole circle (use the formula A = π ×r²) and then divide the answer by 4. Alternatively, you could substitute the radius of the quadrant...

### How to Find the Area of a Quadrant (a Quarter of a Circle)

Finding the modal class from a grouped frequency table is actually quite easy to do. All you need to do is to look for the group that has the highest frequency. This is because the mode is the number that comes up the most times. Make sure you write...

### How to Work out the Modal Class Interval from a Grouped Frequency Table

A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple steps: Step 1: Work out the...

### Compound Shapes: How to Find the Area of an L-Shape

In this hub I will show you how to find the area of circle giving your answer in terms of Pi (π). First of all you need to remember the formula for calculating the area of a circle: A = πr² A stands for area, π stands for Pi and r is...

### Math Help: How to Calculate the Area of Circle and Get an Answer in Terms of Pi

Age and mixture problems are tricky questions in Algebra. It requires deep analytical thinking skills and great knowledge in creating mathematical equations. Practice these age and mixture problems with solutions in Algebra.

### Age and Mixture Problems and Solutions in Algebra

To calculate the 3 point moving averages form a list of numbers, follow these steps: 1. Add up the first 3 numbers in the list and divide your answer by 3. Write this answer down as this is your first 3 point moving average. 2. Add up the next 3...

### How to Calculate the 3 Point Moving Averages from a List of Numbers and Describe the Trend

The nth term of a number sequence is a formula that gives you the values in the numbers sequence from the position number (some people call it the position to term rule). Example 1 Find the nth term of this sequence. 5 8 11 14 17 First of...

### How to Find the nth Term of an Increasing Linear Sequence.

This hub is all about calculating lottery probability or odds. In order to make it relevant, I decided to base it on the Grandlotto 6/55, the lottery game with the biggest prize money here in the Philippines. There will be two different cases in the hub: the probability of winning the game with all six numbers matching, and the probability of having n numbers matching.

### How to Calculate Lottery Probability

Step-by-step guide to multiplying different types of polynomials. Learn how to multiply binomials using the FOIL method. Use the grid method and know why it's the best way to multiply polynomials.

### Multiply Polynomials (With Examples) - FOIL & Grid Method

Learn what trigonometry is and get a view of this area of mathematics throughout history—its development, uses, and why it's important.

### What is Trigonometry? Description & History of Trig

Do you ever wonder how Magic Squares are created? Well, stop worrying. I'll show you how to construct them using just a few easy to follow rules.

### How to create magic squares

The main property of a trapezium (as known in Great Britain) or trapezoid (as known in the United States) is that it is a 4 side shape with exactly one pair of parallel sides. Depending on how the trapezium is drawn determines how many lines of...

### Properties of a trapezium or trapezoid (math facts)

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