Stright lines verses circles

If we take a straight line and roll into a circle the same straight line goes across it once, twice, three times and a little bit more left over. This bit left over is about a 7th.It is 1 dived 7 accurate to 3 decimal places.( 0.142 ).Plus 3 called Pi ( Pie ). Mathematicians have been trying to find the end of the fraction for centuries. In the Genius book of records there are record breaking recitals of pi to many hundreds of places.

All straight lines are reflections of all circles because the same straight lines rolled into circles equals all the circles. Therefore if we measure any straight line with a ruler will be the same circumference when rolled into a circle.

Take a measurement across the rim of a class.( The diameter )

Multiply by pi.

Take a piece of string and measure round the rim, cut to size and open out to a straight line.

When you measure the length of the string with your ruler will agree with the calculation. When you dived the length by pi and check the diameter of the rim of the glass with the ruler agrees.

Circumferences of all circles opened out to straight lines equals the lengths exactly. Knowing the lengths of straight lines we know their circumferences of the circles and knowing the circumferences of circles we the the lengths of the straight lines.

Cut the string in half and measure the length checking the string across the rim of the glass. It will agree form the edge to the center ( called a radius ) of all circles equals to half all straight lines. The circumference of one circle opened out to a straight line will equal the radius of another.

In other wards the radius of one circle will equal the circumference of another. All radii are straight lines equal the circumference of circles Therefore if we know the diameter of a circle is double the length all radi we can use the diameter and pi to calculate a straight line required to create the circle.

Looking at this in another way the circumference of the glass divided in half times pi will result in the circumference of half the size glass. Mathematics tells us this is called a linear scale.

If we take a ruler and bend into a circle the rule divisions will be the same in the circle. Mathematic divides clock faces into 60 minute divisions. So operating on the principle a straight line marked in even 60 divisions rolled into a circle will form the same 60 divisions. Correspondingly math's divides circles into 360 divisions. The same circle opened out to a straight line will equal the same 360 divisions in a straight line.

Thus all divisions in all rulers will equal the same divisions in the circles of the same straight exactly so. Take a glass and string to size the rim with a piece of string and open to a straight line.

Make a mark in half the string. When you roll round the rim of the glass the mark and join will always be opposite corners of each other. If you mark the straight string in quarter increments and roll round the rim of the glass every mark, including the join, will be opposite corners of each other.

Lines drawn down circles divide them clean in half vertically and across them horizontally forming a cross. We can clearly observe of the cross 4 right angle triangles, upper left and right and lower right and left pointing all opposite to each other.

Fold a square piece of paper in half and fold in half again and open out.

You will clearly see the creases form each right angle triangle.

If we mark in 9, 12, 3 and 6 o'clock positions on the cross we form a circle, filling 10,11, 1, 2, 4, 5, 7, and 8 we complete a clock face circle.

When opened out to a straight line numbers dived evenly 9 at the beginning of the straight line, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, and 8 near the end. This straight line forms the horizontal straight line across 9 to 3 of the circle . The straight line plots the positions of the numbers round clock face in a straight line.

When rolled into a circle will agree.

Thus we can mark each O'clock in centimeters forming a 12 centimeter straight line rolled into a clock face.

The smallest typical school ruler division is a millimeter about the width of a typical school circle protractor. Operating on the principle of opening out to a straight line will be a 360mm ruler. Mathematics' expresses all horizontal lines are not angles. The rest are called digress.

Curiosity is the way to learn. Anybody curious enough will wonder how many digress in every minute division of a clock. Curiosity will awaken our mathematical instinct suggests 360 dived 60 equals 6. Proof when we realize 60 times 6 equals 360. Further proof when 6 times 60 equals 360 as 360 divide 6 equals 60 respectively. Mathematics can't lie you know. There for every minute division is a 6 degree angle.

The second hand helps us realize since it is a line from the center to the edge of the circle we can observe it acting as a radius tracing the clock divisions in 6 degree increments.

Beginning with 9 'clock 0 degrees angle 6 degrees is added every second to 90 degrees at 12 O'clock. Going the opposite direction is minus 6 degrees every second till 0 degrees at 3 O'clock.

Going the opposite direction it adds 6 digress every second to 90 digress at 6 O'clock opposite direction to the 90 degrees 12O'clock.

Going the opposite direction every second is a minus 6 degree to 0 degrees at 9 O'clock repeating the circle.

Thus 9 O'clock 0 degrees, 10 O'clock 30 degrees 11 O'clock 60 degrees, 12 O'clock 90 degrees, 1 O'clock 60 degrees, 2 O'clock, 30 digress, 3 O'clock 0 degrees, 4 'clock 30 degrees 5 O'clock 60 degrees, 6 O'clock 90 degrees, 7 O'clock 60 degrees, 8 O'clock, 30 degrees, and finally back to 9 O'clock 0 digress again repeating the circle.

Opened out to a straight line equals 4 times 90, 0 to 90, to 0 to 90, to 0 to 90 to 0 degrees in a full circle each a 90 plot in the straight line plotting right angle triangles, quarters circles, 180 digress half circles, 270 3 quarters to a full in 360 digress and so on.

The same straight line rolled into a circle will represent an upward left and right and a upside down left and right pointing 90 degree right angle triangles. No matte which way the circle will viewed there will always be the triangles.

If a circle cut in half moved half along the circle along the diameter ( axis ) forms a sign wave. The axis is still a straight line comprising of 360 divisions representing 2, 90 degree right angles in a 360 degree circle. The sin wave represents a plus and minus going half of the same circle plotted along the straight line of the axis.

The straight line axis represents the wavelength using the standard metric system prefix unit Hertz. the number of times in a second using the metric prefixes Kilo, for a thousand, Mega for a million and Giga for a thousand million ( HZ, KHz, MHz, GHz respectively )..

Each peak of a sine wave is a wavelength of 90 degrees, 180degrees apart plotted on a straight line of the axis. Two and more waves can be plotted on the same line. Identical waves reinforce each, other, partially out of phase or completely out of phase by a half circle ( 180). In this case the two halves make a whole circle.