Leap Year

A leap year consists of 366 days. During Leap Year, we add a leap day, an extra day on February 29. Leap years are important because we need to keep our calendar in alignment with the Earth's revolutions around the sun. It takes the earth approximately 365.242199 days or 365 days, 5 hours, 48 minutes and 46 seconds to circle once around the sun. However the Gregorian calendar has only 365 days in a year, so if we didn't add a day on February 29 nearly every 4 years, we would lose almost six hours off our calendar every year. After 100 years, our calendar would be off by approximately 24 days!

How to find out that the given year is a leap year?

Any given year is a leap year if it is divisible by 4 but not by 100. If a year is divisible by 4 and by 100, it is not a leap year unless it is also divisible by 400.
For example, years such as 1992, 1996, 1988 and so on are leap years. They are divisible by 4 but not by 100. In case of century years, the 400 rule applies. Thus the century year 1900, though divisible by 4 is not a leap year. It is divisible by 100 but not divisible by 400. The century year 2000 is divisible by 4, is divisible by 100 but also divisible by 400. Thus it is a leap year.

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Magic Square

The ancient Chinese Magic Square was followed by the Lo Shu Square, which dates back to 2200 B.C. It symbolizes the natural order of the Universe, promoting logic, strategy and open-mindedness.

The Legend of Lo Shu
During ancient times in China there was a huge flood on the Lo River. The people tried to calm the River god’s anger by offering sacrifices, but each time they prepared an offering a turtle came up from the river and walked around the sacrifice, and the River god wouldn't accept the sacrifice. This happened several times, until one time, a child noticed curious markings forming a pattern on the turtle’s shell. After studying these markings the people realized the correct amount of sacrifices to make, that is 15. Then the river god was placated. The numbers in every row, up and down, across, or diagonally, add up to 15, which happens to be the number of days it takes for the new moon to become a full moon.
The odd and even numbers alternate in the periphery of the Lo Shu pattern; the 4 even numbers are at the four corners, and the 5 odd numbers (outnumbering the even numbers by one) form a cross in the center of the square. The sums in each of the 3 rows, in each of the 3 columns, and in both diagonals, are all 15 (the number of days in each of the 24 cycles of the Chinese solar year). Since 5 is in the center cell, the sum of any two other cells that are directly through the 5 from each other is 10 (e.g., opposite corners add up to 10.
This pattern, in a certain way, was used by the people in controlling the river. The Lo Shu Square, as the magic square on the turtle shell is called, is the unique normal magic square of order three in which 1 is at the bottom and 2 is in the upper right corner. Every normal magic square of order three is obtained from the Lo Shu by rotation or reflection.
The Square of Lo Shu is also referred to as the Magic Square of Saturn or Chronos.

Cultural significance of the magic square in India
Magic squares have fascinated humanity throughout the ages, and have been around for over 4,120 years. They are found in a number of cultures, including Egypt and India, engraved on stone or metal and worn as talismans, the belief being that magic squares had astrological and divinatory qualities, their usage ensuring longevity and prevention of diseases.

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Tables made easy

You can multiply most of the problems in your head when you know your multiplication table up to 5 times table. If you know your 2, 3, 4 and 5 times tables up to 10 times each number, then you also know part of your 6, 7, 8, and 9 times table. As you learn your higher tables, mental calculations become much easier. It is easy to learn your 11 times table and the twelve times table is not difficult. Six times 12 is six times 10 plus six times two. It is easy to add answers for 6 times 12 to get 72.
6 X 10 = 60; 6 X 2 = 12; 60 + 12 = 72

We see, how easy it is to learn your tables and how it can be done much more quickly than in olden days.
It is usual to learn tables up to the 12 times table. It is not hard to learn the 13 times table if you know the 12 times table. If you know that 12 times 3 is 36, just add another 3 to get 39. Twelve threes plus one more three makes 13 threes. If you know 12 fours are 48. Just add another four to get 13 times 4 equals 52.

Now that you know your 13 times table, learn the 14 times table. Factor 14 to 7 times 2. Then you multiply the number by 7 and double the answer.
7 X 1 = 7; double = 14; 14 X 1 = 14
7 X 2 = 14; double = 28; 14 X 2 = 28
7 X 3 = 21; double = 42; 14 X 3 = 42
7 X 4 = 28; double = 56; 14 X 4 = 56
7 X 5 = 35; double = 70; 14 X 5 = 70
7 X 6 = 42; double = 84; 14 X 6 = 84
7 X 7 = 49; double = 98; 14 X 7 = 98
7 X 8 = 56; double = 112; 14 X 8 = 112
7 X 9 = 63; double = 126; 14 X 9 = 126
7 X 10 = 70; double = 140; 14 X 10 = 140

Practice these easy steps and you will learn your tables without even trying hard. You will find that you can multiply and divide directly by 13, 14 and 15. This will give you an advantage in your Math Class. comments

Fibonacci sequence in sunflower

The arrangement of seeds on the head of a sunflower is a very good example of the Fibonacci sequence. By closely observing the seed configuration we notice two series of curves, one winding in one direction and one in another. The numbers of spirals are not the same in each direction. If we count the number of spirals given in the figure, we notice the number is 21 and the number of spirals in the opposite direction is 34.

Coincidentally, this number is within the Fibonacci sequence. The numbers of spirals are not the same in each direction. In general they are either, 21 and 34, or 34 and 55, or 55 and 89 or 89 and 144. In principle all the sunflowers show a number of spirals that are within the Fibonacci sequence.
For a long time, it had been noticed that these numbers were important in nature, but only relatively recently that one understands why. It is because of the efficiency during the growth process of plants.
In many cases, the head of a flower is made up of small seeds which are produced at the centre, and then migrate towards the outside to fill eventually all the space. Each new seed appears at a certain angle in relation to the preceding one. In order to optimize the filling, it is necessary to choose the most irrational number there is. This number is exactly the golden mean. The corresponding angle, the golden angle is 137.5 degrees. This angle has to be chosen very precisely. Even the variation of 1/10 of a degree destroys the optimization completely. When the angle is exactly the golden mean, two families of spirals (one in each direction) are then visible. Moreover, generally the petals of flower are formed at the extremity of one of the families of spiral. This explains why the number of petals corresponds on average to a Fibonacci number.
We learn that Nature is fortunately a much better Mathematician than most of us.

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Multiplication by 11

We all know that it is easy to multiply a single digit number by 11. If you want to multiply 4 by 11, you simply repeat the digit for the answer, 44. If you multiply 6 by 11, you get 66.
Did you know it is easy to multiply two digit number by 11?
Multiplying a two-digit number by 11.
To multiply 16 by 11, add both the digits of the given number, 1+6 = 7. Now place this answer , 7, in between the two digits, in this case giving you 176.
16 X 11 = 176
These calculations are easy to do in your head. If somebody asks you to multiply 52 by 11, you could immediately say, "five hundred and seventy two".
That was easy! Now, what happens if the digits add to ten or more? comments

Finding age trick

Math tricks are a lot of fun. Students love them in the classroom. We are more open to learning when we are having fun in the process. Math teachers often use number tricks in the classroom to encourage enthusiasm among students. You can use some of these tricks with your friends as well.

A simple trick to find someone's age.
Step 1) Ask your friend to multiply the first number of his age by 5.
Step 2) Now ask him to add 3 to the result.
Step 3) Tell him to double this figure.
Step 4) Finally, ask him to add the second number of his age to the resulting figure and have him tell you the answer.
Step 5) Now you deduct 6 from the answer and you will have his age.

I am sure your friends will be impressed. comments

Number Trick

An interesting trick of number 421. What is so special about the number 421?
Number 421 is the smallest prime number formed by the powers of two in logical order from right to left.

Follow the given steps and you will notice an interesting loop of 4...2...1...
1) Select any whole number.
2) If it is an even number,divide by 2; If it is an odd number, multiply by 3 and add 1 to it.
3) Keep on repeating the process mentioned in step 2. We'll see that after a while the value 4,2,1 repeats itself.

Example: Lets pick a number, say, 23.

23 is an odd number; so multiply by 3 and add 1 to it;
(23 × 3) + 1 = 70
70 is an even number; so divide by 2;
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Funny Calculations

You can play this funny Math trick with your friends. Ask them to do the following calculations and you can predict their date of birth.
1) Add 18 to your Birth month.
2) Multiply by 25.
3) Subtract 333.
4) Multiply by 8.
5) Subtract 554.
6) Divide by 2.
7) Add your Birth date.
8) Multiply by 5.
9) Add 692.
10) Multiply by 20.
11) Add only the last two digits of your Birth year.
12) Subtract 32940 to get your complete date of birth.

Suppose the answer is 102382. This implies that your friend's date of birth is October 23, 1982 (MM/DD/YY).
(Note: If the answer is not right, your friend did not follow the directions correctly or lied about his Birthday.) comments

Fibonacci Numbers

The numbers in the following integer sequence are called the Fibonacci numbers.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two.
1 = 1+0
2 = 1+1
3 = 2+1
5 = 3+2
8 = 5+3
13= 8+5
21= 13+8
34= 21+13
55= 34+21

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Golden Spiral in Nature

"Nature hides her secrets because of her essential loftiness, but not by means of ruse".
~Albert Einstein

  

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Maths in Da Vinci's Art

Leonardo Da Vinci’s most famous illustration is the Vitruvian Man. The figure illustrates the Golden proportion (1:1.618), also known as the ‘Divine proportion’. The Vitruvian Man's drawing is based on the correlations of ideal human proportions. It is accompanied by notes based on the work of the famous first century Roman architect, Vitruvius. He was also the author of ‘De Architectura Libra X’; Vitruvius described the human figure, which was divinely created, as being the principal source of proportion. Leonardo’s drawing is traditionally named in honor of the architect. comments

The beautiful rectangle and the spiral

The Golden Spiral was first discovered by Pythagoras. The spiral is derived from the golden rectangle. When you connect a curve through the corners of these concentric rectangles, the golden spiral is formed.
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The Beauty Of A Rectangle

Look around, you see rectangular objects everywhere, for instance, computer screen, laptops, Desks, Books, Newspaper, cell phones, greeting cards, gift wrappers, paintings, calendars, doors, windows, closets, calculators, towels, bed sheets, photographs, color boxes, note books, dining table, mirrors, credit cards and the list goes on and on. Have you ever wondered why so many people have been drawing and building things that are rectangular shaped?

The ancient Greeks discovered that there is a specifically shaped rectangle that is most pleasing to the eye. It is not too thick, not too thin but just right. The rectangle possessing this characteristic is called the “Golden Rectangle”. If you simply draw what you believe to be the most beautiful rectangle, then measure the lengths of each side and finally divide the longest length by the shortest. You’ll probably find the ratio is somewhere around 1.6, which is called the golden ratio, rounded to the nearest tenth.
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Cool Multiplication

Here's an easy way to find out square of a two digit number.
I) Let's square a two digit number that ends in 5. (without using your calculator :))
For example, we would like to square the number 65.
Step 1: Multiply the first digit of a number with the next number that comes after it. In this case 7 comes after 6.
6x7=42
Step 2: Now place 25 after it.
4225

Well, 65X65 = 4225
By the way, 5 is my favourite number. What's yours?

II) Let's square any two digit number.
For example 27.
Step 1: Look for the nearest ten boundary, which is 30 (27+3=30).
Step 2: Now go down 3 numbers from 27.
=24
Step 3: Multiply 24X30 = 720 (answer 1)
Step 4: 27 is 3 from nearest ten boundary 30
Now square of 3 = 9 (answer 2)
Step 5: Add (answer1) and (answer2)
720+9 = 729

27X27 = 729 comments

Find out on which day you were born?

Have you ever wondered which day of week you were born? I guess yes! So lets find out using simple math to find the day of the week on which you were born.
Finding the month number!
We know that January has 31 days. A week has 7days so every date in February will be 3 days later than the same day in January. (28 is 4 weeks exactly. 28+3=31). For instance, if January 1st of any given year falls on Saturday, February 1st of that year will be 3 days later. That is on Tuesday. Following the same pattern for all the months, the following table is calculated.
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