Mathematics is full of mathematical equations that are highly abstract mouth fills to say the lest.

Algebra teaches us if  straight line of 4mm ( millimeter ) + 8mm = 12mm. This means if 8 + 4 = 12 then  4 + 8 = 12 then 12 - 8 = 4 respectively. So to 12- 4 = 8. This applies to muiltiply. If 4 x 8 = 32, then so to 8 x 4 = 32. If 4 x 8 = 32 then 32 ÷ 8 = 4 and 32 ÷ 4 = 8. Mathematics can't lie you know. For every one equation there is always all four operation options.

Our mathematical instinct agrees if  4mm + ?mm must = 12mm, we can 12 - 4  = giving us 8mm line. Proof of this 8 + 4 = 12 respectively

The same applies to multiplying

If what mm x 12mm must = 36mm we can do 36 ÷ 12 = we need a 3mm long line. Proof of this 12 x 3 = 36 and so on.

Those unfamiliar with the laws of mathematics equations seen abstract and confusing. Equations is not done they sound. Take, one meter plus two meters multiplied by four meters plus eight meters. It certainly sounds the way it's done. Those unfamiliar with the laws of mathematics can be forgiven for attempting to do this sum as it sounds. This is the way it is how it is really done.

1 + 2 = 3

 4 + 8 = 12

   3 x 12 = a total of 36 meters

Algebra teaches us to use Greek and English letters of the alphabet ( a,b,c, x,y.z and so on ), to stand in for numbers instead of using a question mark. Letters in brackets are done first. The muiltiply sign is never used because the letter x  will alternately be confused with the muiltiply sign. So is omitted. Sometimes there is a dot or a dash standing in for it. ( c = 36.  c =  a + b  y + z. ).

Operating on the principle if we muiltiply a number by itself is called a square, such as 5mm x 5mm ( five 5's ) = 25mm expressed as 5 squared millimeters. ( 25²mm).

Operating on the same principle of reversing any equation ( in this case any square ) we have 25 ÷ 5 bringing us back to the root of the square which is 5, called the square root of 25. All square roots is the result of any number. No mater how big.

All calculators have a square key a tick like symbol over any number. ( √ ) It pans out any number is potentially a square. Entering any number pressing the square root key gives the root of that square. For example entering 9 and pressing the square root key gives 3. Proof of this three 3's are 9 ( = 3²  just as 4² is four 4's are 16 the square root of 16 is 4 and so on ).

In this non linear our normal counting including the 0 in uneven numbers, 0 meters,1 meter, 3 meters, 5 meters, 7 meters, 9 meters,11 meters, 13 meters, 15 meters......and so. Even numbers 0 meters, 2 meters, 4 meters, 6 meters, 8 meters, 10 meters, 12 meters, 14 meters...and so on

If we double each number our mathematical instinct tells us 0 doubled can only be 0. But in this application 0 doubled equals 1 plus 1 equals 1. So 0 doubled is 1. One doubled is 2. Two doubled is 4. Four doubled is 8. Eight doubled is 16. Sixteen doubled is 32 and so on. ( 0, 1, 2, 4, 8,16, 32.....and so on )

0 squared accelerates to one meter in a second. One squared two meters in 2 seconds. Two squared 4 meters in 3 seconds. Four squared 16 equals a constant velocity of 16 meters in 4 seconds flat. This is the acceleration rate of the earth's mass pulling on a sky diver in the first several seconds leaving the planes hatch.

Sixteen squared is 32 meters in 5 seconds. Thirty-two squared is 64 meters in 6 seconds. Sixty-four squared 128 meters in 7 seconds and a hundred and twenty eight squared to 256 meters in 8 seconds a total of 0 to 256 meters in 8 seconds flat.

All acceleration must have a terminal acceleration because of the impracticality of infinite acceleration. It is typically the maximum speed limits of sky divers cars and aircrafts. The example given is a terminal acceleration point at 256 meters. In other words 250 meters is quarter kilometer acceleration of just over quarter km in 8 seconds. This is pretty slow about the limit of an average family hatchback. Drag cars can do that in a few seconds much faster than the earth's mass pulls on sky divers.

At those take off's we feel the equivalent to a few kilograms of weight weighing us down into our seats expressed as Gravity Force, we commonly express as G-force in a straight line pulling G's, as Albert Einstein put it the equivalent to a gravity. Boy racers express it showing off the power of their vehicles doing the done.

We feel the earth's mass pulling us to the ground as our normal body weight at rest equivalent to a kilogram of compression per cubic meter the entire bulk of the earth expressed as 1G of the earth's masses acceleration.

Just before sky divers jump out of the planes door the diver experiences the normal 1G. The scientific term is 9.8 Newtown's. When they leap from the plane's door the earth's mass snatches at them to several meters in a second.

It takes about a 120 meters for the average sky diver. After several seconds of accelerating it is terminated to the constant velocity the several meters per per second the same time to reach terminal acceleration. It is the maximum speed limit the earth's mass can pull a diver. It cannot pull them any faster. Terminal acceleration has toped out the acceleration. The average constant velocity is a couple of 100kmph tops.

In any Rolla coaster acceleration if we experience twice our body weight take off is 2G's, 3 times our body weight 3 G's. Four times is the maximum safety limit. Any more pressure effects us. We experience near black outs. Rolla coaster G's must be kept at a maximum of 4 or can potentially stop pace makers and bad hearts.

Algebra teaches us we can use any mathematical information manipulating the laws of mathematics on the numbers we can convert meters per second ( m/s ) into to kmph equivalent ( It is also applied to mph if you like ).

To covert m/s to kmph we know there is 60 seconds in a minute and 60 minutes in an hour. ( In other words sixty 60's ). Our mathematical instinct agrees it is only a matter of 60². In this case 3,600 seconds in an hour.

The standard metric system tells us there is a 1,000 meters in every kilometer. Our mathematical instinct agrees if we walk constantly at a steady pace of a meter every second we end up a distance of 3,600 meters by the time a one hour TV program. In other words, 1m/s = 3,600m/h. If we ignorer the two 0's and replace with a K we walk 3.6kmph throughout the entire time.

If we take a 160kmph ( or a 100mph if you like ) at terminal acceleration we can divide 160 by 3.6. Calculators give us 44 point and endless 4's meters per second constant velocity. Proof of this when we muiltiply 44.44....( all the endless 4's if you like) meters per second by 3.6 gives us a 159 point endless 9'skmph. Acceleration is written as meter per second "per second" not as a square. ( m/s²  ).

Trigonometry says all and every horizontal straight lines is not really an angle.  If horizontal lines are moved vertical has moved moved 90 degrees always a 90 degree angle. The symbol for degrees is the small Greek letter theta θ.

The two straight lines draws a cross, top left and right pointing and bottom right and left pointing right angles. Every corner is a180^θ flip side opposite pointing to each other.

A third line closing of any corner is called a hypotenuse. Mathematics tells a us equal horizontal and vertical lines make a perfect 90^θ  right angle triangle.For the sake of simplicity we will call the vertical line the small letter v, the horizontal line a small h and the Hypotenuse line a capital H. Equal v and h lines the Hypotenuse line always equals a 45^θ  angle.

Algebra teaches us we can manipulate the laws of mathematics with information about perfect right angle triangles named after the ancient Greek discover called Pythagoras.

Draw a equal v and h right angle. It doesn't matter left or right pointing. Or alternatively you can measure a right angle set square with equal sides.

If you measure the lengths of the v line ( or 90^θ  line )  and h ( or 0^θ  ) lines the information will project the length of the hypotenuse line. Pythagoras's theorem tells us..........

Measure the vertical line with a ruler writing down V = ......

Next the horizontal line writing down h = ......

Square each answer writing down h² =...... and V² = ......

Add the two squares.

When you draw to scale the two lines as a single line your ruler agrees. The two sides pans to equal V squared plus h squared

If you enter the square root key completes the theorem giving you the length of the Hypotenuse line. When you measure it with a ruler it agrees with the calculator. H equals the square root of v squared plus h squared. The same rules apply to uneven v and h lines. This works with any left or right pointing right angle.

A mathematical constant in trigonometry is the circumference of a circle and straight lines called pi ( pie ) The Capital Greek letter ( Π ) Theta as it's symbol.

Take a DVD disc. and string. Measure round the circumference with the string and cut to length. When you open out to a straight line measure the length with a ruler. It will tell you 37.7cm ( or 377mm ) long.

This applies to all and every circle the circumference opened up into a straight line and all straight lines rolled into circles equals the circumference of the circle. In other words circumference of circles equal straight lines and straight line equals circumferences of circles.

If you measure across the disc ( diameter, it's width ) will read 120mm. If you measure the string across the disc you will find it will go across once, twice, three times and a little bit more about a 7th. This pans out mathematically to 1 divide 7 plus 3 equals pi but only accurate to 2 decimal places.

Pressing the Π key in scientific calculators displays the accurate value up to 30 decimal places. Mathematicians have been trying to find the end of the fraction for centuries. It appears to be infinite. This fraction never repeats any number, and contains every phone number of the world.

It turns out if we divide the length of the string by Π gives the disc diameter length. Measuring across the disc with your ruler agrees. It turns out the same diameter times Π equals the circumferences of the of the disc. Measuring the length of the string agrees.

Trigonometry divides circles in 360 divisions called degrees. Opened out into a straight line equals the same 360 divisions in the straight line circumference. Thus all and every straight line equals 360^θ of all and every every circle.

This can be proved with repeating the latter on the rim of cups and glasses to coins. It will be true measuring the waist of tin cans with your string. It is also true with spheres. We can measure the circumference of a basket ball with string sniped to length measuring it's length with a ruler, applying the Π formulae tells us the diameter across it.

We can use the string to draw a circle of the ball on paper. Cutting out the circle the ball will sit neatly in it. Π is a formulae used in engineering to engineer machines that require spheres to fit holes perfectly. Trigonometry practices is done on 2-dimensilal drawings of circles and triangles on paper.

If we draw a horizontal line across any circle, divides them clean in half horizontally. If we cut in half along this straight line we create half the circle both halves turns out to equal 180^θ  each

A vehicle doing a U-turn for example is equal to this a straight line across the road that pans out to 1Π. A whole circle back to square one is the other half turns out to be 2Π. Thus a180^θ  U turn equals half the circle equal to 1Π and a complete 360 circle 2Π.

Reviewing the facts, One. Every and all circles open out to straight lines and every and all straight line roll into circles.

Two. Any straight line of interest to be rolled into a circle. Divided by Π pans out to equal the resulting diameter of the circle straight line forms. It pans out the measured length of the diameter multiplied by 2Π equals the both halves of the whole 360^θ  circle.

If we measure a typical 30cm school ruler with string cut to length, dividing the 30cm by Π. Divided in half gives the radius ( from the center to the edge ) 4.77cm long. Rolling the string into a circle or checking out the DVD measurements the length from the center to the edge with the ruler will agrees.

Clock faces are circles, the hands from the center to the edges reflect the radius of every and all circles. Mathematical constants are easy reference material. In this case, every straight line measured by a ruler divided by Π, equals the diameter. Divided in half ( always by 2 ) projects the length of the radius the straight line rolled into.

Algebra teaches us the law of mathematics says we can do the reverse. Taking the 4.77cm radius doubled ( always multiplied by 2 ) equals the diameter of the circle. Multiplied by Π equals to the circumference of the circle. The string and your 30cm long ruler agrees. 

Clock circles are divided into 60 minute divisions while circles 360 divisions. We can work out how many degrees every minute division equals. Our mathematical instinct agrees simply by asking ourselves how may 60's go into 360. ( 360 ÷ 60 = 6 ) pans out every minute division is a 6^θ angle.

Proof of this 60 x 6 = 360. ( sixty, 6's ). The law of mathematics tells us, 360 ÷ 6 = 60. Proof of this 6 x 60 = 360 ( six, 60's ). And 360 ÷  60 = 6 respectively. Proof of this 60 x 6 = 360 respectively Mathematics can't lie you know. It is easy to see from the clock face every 5 minutes adds up to 5 x 6 = 30^θ .10 minutes equals 10 x 6 = 60^θ  and 15 minuets equals 15 x 6 = 90^θ  and so on.

Mathematics tells us both hands across the clock face is equal to a horizontal line, and all horizontal lines are not really angles thus 0 degrees.

If we use the second hand as the radius at 9 O'clock is at a 0^θ  horizontal line. At 10 O'clock is at a 30^θ  angle. At 11 O'clock 60^θ . Dead vertical at 12 O'clock is a 90^θ  angle a quarter circle.

As we observe the second hand pass 12 o'clock it is going the opposite direction. At 1 o'clock it is a 60^θ  angle. 2 O'clock a 30^θ  angle. When at 3 O'clock the hand is at a 0^θ . The hand had rottated180 degrees half circle equal to 1Π

When it is at 4 o'clock is a 30^θ  angle. When at 5 is 60^θ . At 6 o'clock is a 90^θ angle equals three quitter circle ( 270^θ ).

When passing 6 o'clock the hand is going the opposite direction. At 7 is a 60^θ  angle. At 8 is 30^θ  and 3 o'clock completes the circle at 0^θ  equals to a complete 360^θ  circle equal to 2Π.

Thus the second hand acting the radius of any circle measures each corner as 90^θ. If we start with 0^θ at 9 o'clock, we have plus 90 to 12 o'clock. Then there is minus 90 to 3 o'clock equals a flip over of 180^θ. Plus 90^θ  to 6 o'clock and minus 90 to 9 o'clock a flip over of another 180^θ  equals a total 360^θ.

Hands pointing directly horizontally across the clock face is the horizontal diameter. From 12 to 6 a vertical diameter. Pointing directly across from 10 to 4,  11 to 5,  1 to 7 and 2 to 8 are 30 and 60^θ diameters all straight lines.

The minuet hand the small m and the hour hand a small h. So not to confuse the horizontal line with the hour hand the minute hand symbol is the small Greek letter alpha ( α ) and the hour hand the small later beta ( β ).

Mathematics' projects the hour hand is 60 times as slow as the minute hand and 3,600 times as slow as the second hand. The second had acting as a radius plots 6^θ every second flapping 180^θ in a 360^θ arch. The other two hands are stationary at any given moment in time.

When the second hand completes 360^θ the minute hand has only moved 6^θ. Equally when the minute hand completes 360^θ the hour hand has only moved 6^θ.

12 midnight when all hands are pointing to 12 changes the date. Digital clocks tell us no hours, no minutes and no seconds ( 00:00:00 ) for a second. It takes the second hand ½ a minute flip over 180^θ.

It takes the minute hand a ½ hour, and the hour hand 6 hours to make a 180^θ flip over. It takes a minute for the second hand, an hour the minute hand and 12 hours for the hour hand to make a full 360^θ.circle. 360^θ hour hand equals from 12 midnight to 12 midday a.m. and 12 midday to 12 midnight for p.m.

12 midnight 1,  2,  3,  4,  5,  6,  7,  8,  9,  10, 11,  12 in the morning. The afternoon 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, and 12 midnight date change again at 24 hours for p.m.

It takes a total of 23 hours, 59 minutes and 59 seconds for all hands to point to 12 midnight changing the date of a new day. Every position of each hand results in every open ended triangle there is.