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Weird But True! -- Math

Posted by on May. 30, 2013 at 7:09 PM
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Ok, math can be fun too! Here are some of my favorite facts, projects and resources! 

  Articles / Kicbuttmama's Crazy Lapbooks / Kickbuttmama's Home Education
Albert Einstein -- 
   "Everybody is a Genius. But if you judge a fish by its ability to climb a tree, it will spend its whole life believing it is stupid." 

by on May. 30, 2013 at 7:09 PM
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by on May. 30, 2013 at 7:11 PM

  • The numerical digits we use today such as 1, 2 and 3 are based on the Hindu-Arabic numeral system developed over 1000 years ago.

  • Different names for the number 0 include zero, nought, naught, nil, zilch and zip.

  • The smallest ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

  • 2 and 5 are the only prime numbers that end with a 2 or a 5.

  • The golden ratio of approximately 1.618 between two quantities such as lengths often appears in nature (tree branching, uncurling ferns, pine cone arrangements etc) and has been used throughout history to create aesthetically pleasing designs and art works such as Leonardo da Vinci’s Mona Lisa.

  • Fibonacci numbers are named after Italian mathematician Leonardo of Pisa (better known as Fibonacci) who introduced them to Western Europe after they had earlier been described by Indian mathematicians. They are related to the golden ratio and proceed in the following order: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, .... Can you see the pattern?

  • The number Pi (the ratio of the circumference to the diameter of a circle) can’t be expressed as a fraction, making it an irrational number. It never repeats and never ends when written as a decimal.

  • Here is Pi written to 100 decimal places:

  • What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion.

  • The name of the popular search engine ‘Google’ came from a misspelling of the word ‘googol’, which is a very large number (the number one followed by one hundred zeros to be exact).

  • A ‘googolplex’ is the number 1 followed by a googol zeros, a number so ridiculously big that it can’t be written because there literally isn't enough room in the entire universe to fit it in!

  • Check out some more big numbers.

  • You might have heard the word ‘infinity’ before or seen its symbol that looks like the number 8 placed on its side. Infinity means a limitless quantity or something that goes on forever. While it’s not really a number like 1, 2 or 3, infinity is often used in math as part of equations and formulas.

  • 111111111 x 111111111 = 12345678987654321

  • 12 + 3 - 4 + 5 + 67 + 8 + 9 = 100

by on May. 30, 2013 at 7:14 PM

  • A circle is a round, two dimensional shape that looks similar to the letter ‘O’.

  • In strict mathematical language, circle refers to the boundary of the shape while ‘disk’ is used to refer to the whole shape, including the inside.

  • A straight line from the center of a circle to the edge is called the radius.

  • A straight line that passes from one side of a circle to the other through the center is called the diameter.

  • The distance around the outside of a circle is called the circumference.

  • All points on the edge of a circle are the same distance to the center.

  • The value of Pi (π ) to 2 decimal places is 3.14, it comes in handy when working out the circumference and area of a circle.

  • The circumference of a circle can be found with the following formula: Circumference = π d

  • The area of a circle can be found with the following formula: Area = π r²

  • An arc is part of the circumference of a circle.

  • A chord is a straight line joining two points on a circle, the diameter is an example of a chord (the longest possible one).

  • A segment is the region between a chord and the arc it joins.

  • A tangent is a straight line that touches a single point of a circle.

  • A sector is the region between an arc and two radii.

  • The full arc of a circle measures 360 degrees.

  • A semicircle is a shape that forms half a circle, the arc of a semicircle measures 180 degrees.

  • Circles have a high level of symmetry.

  • A circle has the shortest perimeter of all shapes with the same area.

  • The circle shape is a favorite of humans and can be seen in many designs.

  • The invention of the wheel (a circle shape) was one of the most important in human history.

  • Circles and spheres are also frequently seen in nature, can you think of some examples?

by on May. 30, 2013 at 7:15 PM

  • Triangles are polygons with the least possible number of sides (three).

  • The three internal angles of a triangle always add to 180 degrees.

  • An equilateral triangle has three sides of equal length and three equal angles.

  • An isosceles triangle has two sides of equal length and two equal angles.

  • A scalene triangle has no sides of equal length and no equal angles.

  • A right angle triangle has one angle that is 90 degrees.

  • An obtuse triangle has one angle larger than 90 degrees.

  • An acute triangle has angles that are all less than 90 degrees.

    The longest side of a right angle triangle is called the hypotenuse, it is always found opposite the right angle.

  • Trigonometry is the study of the relationship between the angles of triangles and their sides.

  • Triangle shapes are often used in construction because of their great strength.

  • Now that you're an expert on triangles, try learning about squares,quadrilaterals and other 2D polygon shapes.
by on May. 30, 2013 at 7:16 PM

  • A square is a polygon with 4 sides of equal length and 4 right angle corners (90 degree corners).

  • Because it has 4 sides of equal length, a square is a regular quadrilateral.

  • A square is also a rectangle with equal sides and a rhombus with right angles.

  • The area of a square is equal to the length of one side to the power of two (length squared).

  • The perimeter of a square is 4 times the length of one side.

  • A square has a larger area than all other quadrilaterals with the same perimeter.

  • The diagonals of a square bisect each other at 90 degrees and are perpendicular.

  • Opposite sides of a square are parallel.

  • The internal angles of a square add to 360 degrees.

  • A square has 4 lines of reflectional symmetry.

  • Square shapes are often used by humans for design and engineering purposes such as town planning.

  • cube features six square faces and in many ways is like a square, only in three dimensions rather than two.

  • Now that you're an expert on squares, try learning about triangles and other 2D polygon shapes.


by on May. 30, 2013 at 7:16 PM

  • A quadrilateral is a polygon with 4 sides and 4 corners.

  • The word ‘quadrilateral’ comes from ‘quad’ meaning ‘4’ and ‘lateral’ meaning ‘of sides’.

  • The interior angles of quadrilaterals add to 360 degrees.

  • Any quadrilateral with 4 right angles is a rectangle.

  • A quadrilateral with 4 right angles and 4 equal length sides is a square.
    The area of a square is equal to the length of one side to the power of two (length squared).

  • The perimeter of a square is 4 times the length of one side.

  • Quadrilaterals with 2 sets of parallel side are called parallelograms.

  • A rhombus is a quadrilateral with four sides of the same length. A diamond shape is a good example of a rhombus.

  • A convex (outward) quadrilateral with one pair of parallel sides is known as a trapezoid in the US and a trapezium in other parts of the world. In both instances it comes from a Greek word meaning ‘a little table’.

  • A kite quadrilateral features 2 pairs of adjacent sides that are of equal length (much like a kite you can fly in the sky).

  • Check out our pictures of shapes.

by on May. 30, 2013 at 7:17 PM

  • Greek philosopher and mathematician Pythagoras lived around the year 500 BC and is known for his Pythagorean theorem relating to the three sides of a right angle triangle: a² + b² = c²

  • Greek mathematician Euclid is often referred to as the ‘Father of Geometry’ for his revolutionary ideas and influential textbook called ‘Elements’ that he wrote around the year 300 BC.

  • Archimedes of Syracuse lived around the year 250 BC and among other things, developed a method for determining the volume of objects with irregular shapes.

  • Italian mathematician Leonardo of Pisa (better known as Fibonacci) lived between the years 1170 and 1250 and is best known today for Fibonacci numbers, the number sequence named after him. Fibonacci introduced the number sequence to Western Europe in his book ‘Liber Abaci’ after they had been described earlier by Indian mathematicians.

  • The Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ....

  • In the 17th century Galileo Galilei and Johannes Kepler made important discoveries relating to planetary motion and orbits.

  • German mathematician Gottfried Leibniz lived between 1646 and 1716, developing important calculus concepts and mathematical notation practices.

  • Isaac Newton discovered the laws of physics and brought together many important concepts of infinitesimal calculus.

  • Much of the work done by Leibniz and Newton is based on theories by French philosopher Rene Descartes. As well as his many contributions to philosophy, Descartes also had a huge impact on mathematics, creating analytical geometry, developing a system that describes geometry using algebra, contributing to optics and much more.

  • Born in France, Pierre de Fermat was an amateur mathematician who is best known for Fermat’s Last Theorem.

  • In 1642 French mathematician Blaise Pascal invented the mechanical calculator.

  • Swiss mathematician Leonhard Euler was probably the most influential mathematician of the 18th century, making discoveries in graph theory and introducing many modern mathematical words and notations among other things.

  • Born in 1777, German mathematician Carl Friedrich Gauss contributed brilliant work in geometry, statistics, number theories, algebra and much more.

  • Bernhard Riemann was an influential German mathematician who contributed to differential geometry and analysis, paving the way for the development of general relativity by Albert Einstein.

  • Born in 1882, Emmy Noether was a German mathematician who made important contributions to abstract algebra and theoretical physics, described by Einstein as the most important woman in the history of mathematics.

  • Alan Turing was a British mathematician and computer scientist who cracked German ciphers (codes) in the Second World War, contributed to mathematical logic and played an important role in the development of algorithms, artificial intelligence and the modern computer.

  • Born in 1953, British mathematician Andrew Wiles is most famous for proving Fermat’s Last Theorem.

by on May. 30, 2013 at 7:18 PM

  • I am an odd number. Take away one letter and I become even. What number am I? 

    Answer: Seven (take away the ‘s’ and it becomes ‘even’).

  • Using only addition, how do you add eight 8’s and get the number 1000? 

    Answer: 888 + 88 + 8 + 8 + 8 = 1000

  • Sally is 54 years old and her mother is 80, how many years ago was Sally’s mother three times her age? 

    Answer: 41 years ago, when Sally was 13 and her mother was 39.

  • Which 3 numbers have the same answer whether they’re added or multiplied together? 

    Answer: 1, 2 and 3.

  • There is a basket containing 5 apples, how do you divide the apples among 5 children so that each child has 1 apple while 1 apple remains in the basket? 

    Answer: 4 children get 1 apple each while the fifth child gets the basket with the remaining apple still in it.

  • There is a three digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number? 

    Answer: 141

  • What word looks the same backwards and upside down? 

    Answer: SWIMS

  • Two girls were born to the same mother, at the same time, on the same day, in the same month and in the same year and yet somehow they’re not twins. Why not? 

    Answer: Because there was a third girl, which makes them triplets!

  • A ship anchored in a port has a ladder which hangs over the side. The length of the ladder is 200cm, the distance between each rung in 20cm and the bottom rung touches the water. The tide rises at a rate of 10cm an hour. When will the water reach the fifth rung? 

    Answer: The tide raises both the water and the boat so the water will never reach the fifth rung.

by on May. 30, 2013 at 7:18 PM

  • 111111111 x 111111111 = 12345678987654321

  • 12 + 3 - 4 + 5 + 67 + 8 + 9 = 100

  • 1 x 8 + 1 = 9
    12 x 8 + 2 = 98
    123 x 8 + 3 = 987
    1234 x 8 + 4 = 9876
    12345 x 8 + 5 = 98765
    123456 x 8 + 6 = 987654
    1234567 x 8 + 7 = 9876543
    12345678 x 8 + 8 = 98765432
    123456789 x 8 + 9 = 987654321

  • The number 142857 is rather special. When you multiply it the digits found in the answer stay the same, just in a different order. Check it out:

    1 x 142857 = 142857
    2 x 142857 = 285714
    3 x 142857 = 428571
    4 x 142857 = 571428
    5 x 142857 = 714285
    6 x 142857 = 857142

    What happens when you multiply it by 7? You get another rather special number:

    7 x 142857 = 999999

    And it doesn't stop there:

    142 + 857 = 999
    14 + 28 + 57 = 99

    142857 x 142857 = 20408122449
    20408 + 122449 = 142857

    That’s one amazing number!
    by on May. 30, 2013 at 7:19 PM

    • It is believed that Ancient Egyptians used complex mathematics such as algebra, arithmetic and geometry as far back as 3000 BC, such as equations to approximate the area of circles.

    • Babylonians measured the circumference of a circle as approximately 3 times the diameter, which is fairly close to today’s measurement which uses the value of Pi (around 3.14).

    • Chinese mathematics developed around the 11th century BC and included important concepts related to negative numbers, decimals, algebra and geometry.

    • Greek mathematics developed from around the 7th century BC, producing many important theories thanks to great mathematicians such as Pythagoras, Euclid and Archimedes.

    • The Hindu-Arabic numeral system began developing as early as the 1st century with a full system being established around the 9th century, forming the basis of the numerical digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 that we use today.

    • The symbols used for addition (+) and subtraction (-) have been around for thousands of years but it wasn't until the 16th century that most mathematical symbols were invented. Before this time math equations were written in words, making it very time consuming.

    • The equals sign (=) was invented in 1557 by a Welsh mathematician named Robert Recorde.

    • Mathematical developments increased rapidly around the time of the Italian Renaissance in the 16th century and continued through the scientific revolution of the 17th and 18th centuries, becoming increasingly abstract in the 19th and 20th centuries.

    • The basic arithmetic operations used in mathematics are addition, subtraction, multiplication and division.

    • Modern mathematics has advanced greatly thanks to the incredible computing power of today’s computers.

    • These days mathematics is important in many different types of jobs, including those related to engineering, business, science, medicine and more.

    by on May. 30, 2013 at 7:28 PM

    1 = One
    10 = Ten
    100 = One hundred
    1000 = One thousand
    86400 = The number of seconds in a day
    1000000 = One million
    31556926 = The number of seconds in a year
    1000000000 = One billion
    7000000000 = The estimated human population on Earth (2011)
    1000000000000 = One trillion
    1000000000000000 = One quadrillion
    1000000000000000000 = One quintillion
    1000000000000000000000 = One sextillion
    1000000000000000000000000 = One septillion
    1000000000000000000000000000 = One octillion
    1000000000000000000000000000000 = One nonillion
    1000000000000000000000000000000000 = One decillion
    1000000000000000000000000000000000000 = One undecillion
    1000000000000000000000000000000000000000 = One duodecillion
    1000000000000000000000000000000000000000000 = One tredecillion
    1000000000000000000000000000000000000000000000 = One quattuordecillion
    1000000000000000000000000000000000000000000000000 = One quindecillion
    1000000000000000000000000000000000000000000000000000 = One sexdecillion
    1000000000000000000000000000000000000000000000000000000 = One septendecillion
    1000000000000000000000000000000000000000000000000000000000 = One octodecillion
    1000000000000000000000000000000000000000000000000000000000000 = One novemdecillion
    1000000000000000000000000000000000000000000000000000000000000000 = One vigintillion

    0000000000000000000000000000000000 = One googol (the number 1 followed by 100 zeros)

    000000000000000000000000 = One centillion (the number 1 followed by 303 zeros)

    One googolplex = The number 1 followed by a googol zeros (there literally isn't enough room in the universe to write this number).

    While not really a number, ‘infinity’ refers to a limitless quantity and is represented by a symbol that looks like the number 8 placed on its side

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