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Ahatmose Wrote:
-------------------------------------------------------
> PLEASE NOTE:
>
> 36 / 11.46 = Pi not 36 / 14
>
> Cheers
> db
>
What is Pi?
Pi is the ratio that is based upon the circumference of a circle divided by the circle’s diameter. There are 3 values for Pi. The first value for Pi is 3.141592653589793. The first version of Pi can be obtained if 1759.2918860102842 is divided by 560. The second version of Pi is 3.146446609406726 and can be obtained if 14 is subtracted from the Square root of 2 = 1.414213562373095 resulting in 12.585786437626905 and if 12.585786437626905 is divided by 4 then the second value of Pi 3.146446609406726 can be obtained. The third value for Pi is 3.144605511029693 and can be obtained if the Golden ratio of 1.618033988749895 that is obtained from Cosine (36) x 2 is then applied to Square root and the result = 1.272019649514069 is then 4 is divided by 1.272019649514069 resulting in the third modern value for Pi = 3.144605511029693. There is a debate among scholars regarding which version of the 3 values of Pi are better to use when dealing with circles and geometrical figures. The view of this author is that all 3 of the values of Pi are important and all the 3 values of Pi must be studied as much as possible to achieve accuracy. The 3 values of Pi 3.141592653589793 and 3.146446609406726 and 3.144605511029693 must be compared to each other so the geometrician can determine which value is best suited for the desired task. The author of this book does not like to use the modern versions of Pi to only read the circumference of a circle compared to the diameter of a circle alone because the modern versions of Pi do not allow the circumference of a circle to be read and identified properly with no decimal points. If the modern versions of Pi are used to obtain the circumference of a circle then an infinite amount of decimal places will also be shown with the calculation and this is not good. Instead of using the modern versions of Pi to solely read the circumference of a circle in relation to the diameter of the circle approximations of the 3 modern versions of Pi must be used to know the measure for a circle’s circumference in relation to its diameter. Approximations for the 3 modern versions of Pi can be discovered when the readings given to us by the 3 modern versions of Pi are reduced to 4 or 5 decimal places. The author of this book prefers to use the 13 ancient versions of the versions of Pi. All the 13 ancient versions of Pi are approximations of the 3 modern versions of Pi. The circumference of a circle can be numerically known exactly 100% if any of the 13 ancient versions of the 3 versions of Pi are multiplied accordingly to the order of there appearance below by the measurement for the diameter of circles that have diameters that are capable of being divided into 14 equal units of measure or 13.75 equal units of measure or 11.3 equal units of measure or 11.46 equal units of measure or 8.9 equal units of measure or 5.09295 equal units of measure or 39.78 or 15.91 or 12.7325 or 21.2. 864000 or 7920 or 12756.319 equal units of measure. There are many more approximations of modern Pi that allow the circumference of a circle when divided by and compared to the diameter of the circle to be known, but the author of this book has chosen to only promote 13 of the most common approximations of Pi.
• 22 divided by 7 is 1 of the approximations of Pi 3.142857142857143 that properly allows the circumference of a circle to be read and identified properly with no infinite amount of decimal places regarding the measure for the circle’s circumference and also the circle’s diameter when the circle’s diameter is capable of being divided into 14 equal units of measure.
• 864 divided by 275 = 3.141818181818182 and this is the second method that the author of this book promotes for finding the measure of a circle’s circumference in relation to it’s diameter with 100% accuracy, this second method of Pi works when the diameter of the circle is capable of being divided into 13.75 equal units of measure.
• 355 divided by 113 = 3.141592920353982 and is the third method of approximating Pi for the purpose of 100% accurately finding the measurement for the circumference of a circle in relation to the measurement for the diameter of the circle that the author of this book is promoting. The third method Pi works when the diameter of a circle is capable of being divided into 11.3 equal units of measure.
• The fourth method of obtaining an ancient version of Pi is 36 divided by 11.46 or 360 divided by 114.6 = 3.141361256544503. The fourth ancient version of Pi works with numbers that are a multiple of 18 or divisible by 18.
• The fifth ancient version of Pi only works if the circumference of a circle is 28 or any multiple of 28 and is also divisible by 28, while the diameter of the circle is 8.9 or is any multiple of 8.9 or is divisible by 8.9. The fifth version of Pi numerically is 3.146067415730337 and is the result of 28 divided by 8.9.
• The sixth ancient version of Pi only works if the circumference of a circle is 16 or any multiple of 16 and is also divisible by 16, while the diameter of the circle is 5.09295 or is any multiple of 5.09295 or is divisible by 5.09295. The sixth ancient version of Pi numerically is 3.141597698779686 and is the result of 16 divided by 5.09295.
• The seventh ancient version of Pi only works if the circumference of a circle is 125 or any multiple of 125 and is also divisible by 125, while the diameter of the circle is 39.78 or is any multiple of 39.78 or is divisible by 39.78. The eighth ancient version of Pi numerically is 3.14228255404726 and can be if 125 is divided by 39.78.
• The eighth ancient version of Pi only works if the circumference of a circle is 50 or any multiple of 50 and is also divisible by 50, while the diameter of the circle is 15.91 or is any multiple of 15.91 or is divisible by 15.91.The eighth ancient version of Pi numerically is 3.142677561282212 and can be obtained if 50 is divided by 15.91.
• The ninth ancient version of Pi only works if the circumference of a circle is 40 or any multiple of 40 and is also divisible by 40, while the diameter of the circle is 12.7325 or is any multiple of 12.7325 or is divisible by 12.735.The ninth ancient version of Pi numerically is 3.141566856469664 and can be obtained if 40 is divided by 12.7325.
• The tenth ancient version of Pi only works if the circumference of a circle is 66.6 or any multiple of 66.6 and is also divisible by 66.6, while the diameter of the circle is 21.2 or is any multiple of 21.2 or is divisible by 21.2.The tenth ancient version of Pi numerically is 3.141509433962264 and can be obtained if 666 is divided by 212 or 66.6 is divided by 21.2.
• The eleventh ancient version of Pi only works if the circumference of a circle is 2714336 or any multiple of 2714336 and is also divisible by 2714336, while the diameter of the circle is 864000 or is any multiple of 864000 or is divisible by 864000.The tenth ancient version of Pi numerically is 3.141592592592593 and can be obtained if 2714336 is divided by 864000.
• The twelfth ancient version of Pi only works if the circumference of a circle is 24881.41 or any multiple of 24881.41 and is also divisible by 24881.41, while the diameter of the circle is 7920 or is any multiple of 7920 or is divisible by 7920.The twelfth ancient version of Pi numerically is 3.141592171717172 and can be obtained if 24881.41 is divided by 7920.
• The thirteenth ancient version of Pi only works if the circumference of a circle is 40075.16 or any multiple of 40075.16 and is also divisible by 40075.16, while the diameter of the circle is 12756.319 or is any multiple of 12756.319 or is divisible by 12756.319.The thirteenth ancient version of Pi numerically is 3.141592805887027, and can be obtained if 40075.16 is divided by 12756.319.
“Using Pi to know the circumference of a circle when only the measure for the diameter is known”:
The circumference of a circle can also be known if Pi is multiplied by the measure for the diameter of the circle.
“Using Pi to know the measure for the diameter of a circle when only the measure for the circumference of the circle is known:”
If the circumference of a circle is divided by Pi then the measure for the circle’s diameter can then be known.
“Calculating Pi by dividing half the circle’s circumference by the radius of the circle”:
The ratio Pi can also be approximated when half of a circles’ circumference is divided by the radius of the circle.
“Tau is the circumference of a circle divided by the radius of the circle”:
The circumference of a circle can also be known if Pi is multiplied twice and then multiplied by the measure for the radius of the circle. The circumference of a circle divided by the radius of a circle is known as Tau and is the result of Pi being multiplied 2 equal times.
“Obtaining a quarter of a circle’s circumference with half of Pi”:
A quarter of a circle’s circumference can be obtained also if half of Pi is multiplied by the radius of the circle. Remember to use the correct approximation of Pi for the measure of the circle’s circumference that you want. To know
“Calculating Pi by using the edges of multiple polygons in a circle”:
One of the numerous methods for geometrically approximating Pi is the method of the Deceased ancient Greek Mathematician Archimedes. Archimedes’ method for approximating Pi includes dividing the circumference of a circle into multiple polygons by multiplying the divisions of the circle’s circumference such as beginning with the division of the circle’s circumference into 6 and then 12 and then 24 and then 48 and then 96. The higher the division the closer the approximation of Pi will be. Applications for PI include calculating the mass of circular and spherical objects.
“Calculating Pi by multiplying the divisions of a circle across the diameter of a circle”:
Alternatively Pi can be obtained Geometrically when the circumference of a circle is divided into any number that is divisible by 360. To obtain the most accuracy the arcs that divide the circle can de divided into 100 equal units of measure each so that fractions can also be obtained. To obtain Pi Geometrically the circumference of a circle can be divided into any number that is divisible by 360 and then multiplying that measure along the diameter of the circle so the measurement of the circle’s circumference can be compared and divided by the diameter of the circle.
“Using Pi to calculate the area of a circle”;
Pi can also be used to find the area of a circle and this formula reads any version of Pi multiplied by the radius of the circle and then the result of Pi being multiplied by the radius of the circle is then multiplied by the radius of the circle. So a circle with a radius of 4.5 has an area of 63.617251235193308 according to the modern version of Pi.
If the area of a circle is already known and the desire is to then know the measure for the radius of the circle the measure for the area of the circle should be divided by Pi and then the result must be applied to square root and then an approximation for the circle’s radius can be given and the approximation for the circle’s radius must be educed to 4 decimal places and then 0.01 can be added to the whole value to determine the correct measure for the circle’s radius or alternatively 1 can be added to the last of the 4 decimal digits. Pi is approximated when all the decimal places are reduced to 4 or 5 decimal places. The correct approximation of Pi is determined by multiplying Pi by the measure of the diameter of the circle and then dividing the result of multiplying Pi by the circle’s diameter by the measure of the circle’s diameter after the results that are given to us by traditional Pi are reduced to 4 decimal places. If the diameter of a circle is 11.46 equal units of measure then the surface area of the circle with a diameter of 11.46 equal units of measure 1s 103.14 equal units of measure according to Pi approximated to: 36 divided by 11.46 = 3.141361256544503.
“Discovering more approximations of modern Pi the many other versions of Pi”:
More approximations of Pi can be discovered by reducing the results that are given from dividing the circumference of a circle by modern Pi to 4 or 5 decimal places. The result will be the radius of the circle squared when the area of the circle is divided by Pi. The value for the radius of the circle squared must then be applied to square root and then the measure for the radius of the circle can then be known. Remember to reduce the decimal places to 2 or 3 or 4 digits if the result involves an infinite amount of decimal places. Also if the desire is to have the result read as a whole number 0.1 can be added to a value that is reduced to 3 decimal digits and ends in 0.99. Remember that the radius of a circle is half of the diameter of a circle.
“Using Pi to find the surface area of a Sphere”:
Pi can also be used to find the surface area of a Sphere. A sphere is a 3-dimensional version of a circle. A circle is 2-dimensional.
To find the surface area of Sphere first create a circle with the same diameter of measure as the Sphere and then discover the area of that circle and the surface are of a Sphere is 4 times larger than the area of a circle with a diameter of equal measure to the diameter of the Sphere.
Alternatively the surface area of a Sphere can be found with the following steps:
1. Know the parts of the equation, Surface Area = 4πr2. ...
2. Find the radius of the sphere. ...
3. Square the radius by multiplying it by itself. ...
4. Multiply this result by 4. ...
5. Multiply the results by pi (π). ...
6. Remember to add your units to the final answer. ...
7. Practice with an example. ...
Understand surface area.
“Using Pi to find the volume of a Sphere”:
“The volume of a Sphere can also be found by involving Pi in the equation” by following the steps proceeding”:
1.Write down the equation for calculating the volume of a sphere. This is the equation: V = ⁴⁄₃πr³. ...
2.Find the radius. If you're given the radius, then you can move on to the next step. ...
3.Cube the radius. ...
4.Multiply the cubed radius by 4/3. ...
5.Multiply the equation by π.
>
-------------------------------------------------------
> PLEASE NOTE:
>
> 36 / 11.46 = Pi not 36 / 14
>
> Cheers
> db
>
What is Pi?
Pi is the ratio that is based upon the circumference of a circle divided by the circle’s diameter. There are 3 values for Pi. The first value for Pi is 3.141592653589793. The first version of Pi can be obtained if 1759.2918860102842 is divided by 560. The second version of Pi is 3.146446609406726 and can be obtained if 14 is subtracted from the Square root of 2 = 1.414213562373095 resulting in 12.585786437626905 and if 12.585786437626905 is divided by 4 then the second value of Pi 3.146446609406726 can be obtained. The third value for Pi is 3.144605511029693 and can be obtained if the Golden ratio of 1.618033988749895 that is obtained from Cosine (36) x 2 is then applied to Square root and the result = 1.272019649514069 is then 4 is divided by 1.272019649514069 resulting in the third modern value for Pi = 3.144605511029693. There is a debate among scholars regarding which version of the 3 values of Pi are better to use when dealing with circles and geometrical figures. The view of this author is that all 3 of the values of Pi are important and all the 3 values of Pi must be studied as much as possible to achieve accuracy. The 3 values of Pi 3.141592653589793 and 3.146446609406726 and 3.144605511029693 must be compared to each other so the geometrician can determine which value is best suited for the desired task. The author of this book does not like to use the modern versions of Pi to only read the circumference of a circle compared to the diameter of a circle alone because the modern versions of Pi do not allow the circumference of a circle to be read and identified properly with no decimal points. If the modern versions of Pi are used to obtain the circumference of a circle then an infinite amount of decimal places will also be shown with the calculation and this is not good. Instead of using the modern versions of Pi to solely read the circumference of a circle in relation to the diameter of the circle approximations of the 3 modern versions of Pi must be used to know the measure for a circle’s circumference in relation to its diameter. Approximations for the 3 modern versions of Pi can be discovered when the readings given to us by the 3 modern versions of Pi are reduced to 4 or 5 decimal places. The author of this book prefers to use the 13 ancient versions of the versions of Pi. All the 13 ancient versions of Pi are approximations of the 3 modern versions of Pi. The circumference of a circle can be numerically known exactly 100% if any of the 13 ancient versions of the 3 versions of Pi are multiplied accordingly to the order of there appearance below by the measurement for the diameter of circles that have diameters that are capable of being divided into 14 equal units of measure or 13.75 equal units of measure or 11.3 equal units of measure or 11.46 equal units of measure or 8.9 equal units of measure or 5.09295 equal units of measure or 39.78 or 15.91 or 12.7325 or 21.2. 864000 or 7920 or 12756.319 equal units of measure. There are many more approximations of modern Pi that allow the circumference of a circle when divided by and compared to the diameter of the circle to be known, but the author of this book has chosen to only promote 13 of the most common approximations of Pi.
• 22 divided by 7 is 1 of the approximations of Pi 3.142857142857143 that properly allows the circumference of a circle to be read and identified properly with no infinite amount of decimal places regarding the measure for the circle’s circumference and also the circle’s diameter when the circle’s diameter is capable of being divided into 14 equal units of measure.
• 864 divided by 275 = 3.141818181818182 and this is the second method that the author of this book promotes for finding the measure of a circle’s circumference in relation to it’s diameter with 100% accuracy, this second method of Pi works when the diameter of the circle is capable of being divided into 13.75 equal units of measure.
• 355 divided by 113 = 3.141592920353982 and is the third method of approximating Pi for the purpose of 100% accurately finding the measurement for the circumference of a circle in relation to the measurement for the diameter of the circle that the author of this book is promoting. The third method Pi works when the diameter of a circle is capable of being divided into 11.3 equal units of measure.
• The fourth method of obtaining an ancient version of Pi is 36 divided by 11.46 or 360 divided by 114.6 = 3.141361256544503. The fourth ancient version of Pi works with numbers that are a multiple of 18 or divisible by 18.
• The fifth ancient version of Pi only works if the circumference of a circle is 28 or any multiple of 28 and is also divisible by 28, while the diameter of the circle is 8.9 or is any multiple of 8.9 or is divisible by 8.9. The fifth version of Pi numerically is 3.146067415730337 and is the result of 28 divided by 8.9.
• The sixth ancient version of Pi only works if the circumference of a circle is 16 or any multiple of 16 and is also divisible by 16, while the diameter of the circle is 5.09295 or is any multiple of 5.09295 or is divisible by 5.09295. The sixth ancient version of Pi numerically is 3.141597698779686 and is the result of 16 divided by 5.09295.
• The seventh ancient version of Pi only works if the circumference of a circle is 125 or any multiple of 125 and is also divisible by 125, while the diameter of the circle is 39.78 or is any multiple of 39.78 or is divisible by 39.78. The eighth ancient version of Pi numerically is 3.14228255404726 and can be if 125 is divided by 39.78.
• The eighth ancient version of Pi only works if the circumference of a circle is 50 or any multiple of 50 and is also divisible by 50, while the diameter of the circle is 15.91 or is any multiple of 15.91 or is divisible by 15.91.The eighth ancient version of Pi numerically is 3.142677561282212 and can be obtained if 50 is divided by 15.91.
• The ninth ancient version of Pi only works if the circumference of a circle is 40 or any multiple of 40 and is also divisible by 40, while the diameter of the circle is 12.7325 or is any multiple of 12.7325 or is divisible by 12.735.The ninth ancient version of Pi numerically is 3.141566856469664 and can be obtained if 40 is divided by 12.7325.
• The tenth ancient version of Pi only works if the circumference of a circle is 66.6 or any multiple of 66.6 and is also divisible by 66.6, while the diameter of the circle is 21.2 or is any multiple of 21.2 or is divisible by 21.2.The tenth ancient version of Pi numerically is 3.141509433962264 and can be obtained if 666 is divided by 212 or 66.6 is divided by 21.2.
• The eleventh ancient version of Pi only works if the circumference of a circle is 2714336 or any multiple of 2714336 and is also divisible by 2714336, while the diameter of the circle is 864000 or is any multiple of 864000 or is divisible by 864000.The tenth ancient version of Pi numerically is 3.141592592592593 and can be obtained if 2714336 is divided by 864000.
• The twelfth ancient version of Pi only works if the circumference of a circle is 24881.41 or any multiple of 24881.41 and is also divisible by 24881.41, while the diameter of the circle is 7920 or is any multiple of 7920 or is divisible by 7920.The twelfth ancient version of Pi numerically is 3.141592171717172 and can be obtained if 24881.41 is divided by 7920.
• The thirteenth ancient version of Pi only works if the circumference of a circle is 40075.16 or any multiple of 40075.16 and is also divisible by 40075.16, while the diameter of the circle is 12756.319 or is any multiple of 12756.319 or is divisible by 12756.319.The thirteenth ancient version of Pi numerically is 3.141592805887027, and can be obtained if 40075.16 is divided by 12756.319.
“Using Pi to know the circumference of a circle when only the measure for the diameter is known”:
The circumference of a circle can also be known if Pi is multiplied by the measure for the diameter of the circle.
“Using Pi to know the measure for the diameter of a circle when only the measure for the circumference of the circle is known:”
If the circumference of a circle is divided by Pi then the measure for the circle’s diameter can then be known.
“Calculating Pi by dividing half the circle’s circumference by the radius of the circle”:
The ratio Pi can also be approximated when half of a circles’ circumference is divided by the radius of the circle.
“Tau is the circumference of a circle divided by the radius of the circle”:
The circumference of a circle can also be known if Pi is multiplied twice and then multiplied by the measure for the radius of the circle. The circumference of a circle divided by the radius of a circle is known as Tau and is the result of Pi being multiplied 2 equal times.
“Obtaining a quarter of a circle’s circumference with half of Pi”:
A quarter of a circle’s circumference can be obtained also if half of Pi is multiplied by the radius of the circle. Remember to use the correct approximation of Pi for the measure of the circle’s circumference that you want. To know
“Calculating Pi by using the edges of multiple polygons in a circle”:
One of the numerous methods for geometrically approximating Pi is the method of the Deceased ancient Greek Mathematician Archimedes. Archimedes’ method for approximating Pi includes dividing the circumference of a circle into multiple polygons by multiplying the divisions of the circle’s circumference such as beginning with the division of the circle’s circumference into 6 and then 12 and then 24 and then 48 and then 96. The higher the division the closer the approximation of Pi will be. Applications for PI include calculating the mass of circular and spherical objects.
“Calculating Pi by multiplying the divisions of a circle across the diameter of a circle”:
Alternatively Pi can be obtained Geometrically when the circumference of a circle is divided into any number that is divisible by 360. To obtain the most accuracy the arcs that divide the circle can de divided into 100 equal units of measure each so that fractions can also be obtained. To obtain Pi Geometrically the circumference of a circle can be divided into any number that is divisible by 360 and then multiplying that measure along the diameter of the circle so the measurement of the circle’s circumference can be compared and divided by the diameter of the circle.
“Using Pi to calculate the area of a circle”;
Pi can also be used to find the area of a circle and this formula reads any version of Pi multiplied by the radius of the circle and then the result of Pi being multiplied by the radius of the circle is then multiplied by the radius of the circle. So a circle with a radius of 4.5 has an area of 63.617251235193308 according to the modern version of Pi.
If the area of a circle is already known and the desire is to then know the measure for the radius of the circle the measure for the area of the circle should be divided by Pi and then the result must be applied to square root and then an approximation for the circle’s radius can be given and the approximation for the circle’s radius must be educed to 4 decimal places and then 0.01 can be added to the whole value to determine the correct measure for the circle’s radius or alternatively 1 can be added to the last of the 4 decimal digits. Pi is approximated when all the decimal places are reduced to 4 or 5 decimal places. The correct approximation of Pi is determined by multiplying Pi by the measure of the diameter of the circle and then dividing the result of multiplying Pi by the circle’s diameter by the measure of the circle’s diameter after the results that are given to us by traditional Pi are reduced to 4 decimal places. If the diameter of a circle is 11.46 equal units of measure then the surface area of the circle with a diameter of 11.46 equal units of measure 1s 103.14 equal units of measure according to Pi approximated to: 36 divided by 11.46 = 3.141361256544503.
“Discovering more approximations of modern Pi the many other versions of Pi”:
More approximations of Pi can be discovered by reducing the results that are given from dividing the circumference of a circle by modern Pi to 4 or 5 decimal places. The result will be the radius of the circle squared when the area of the circle is divided by Pi. The value for the radius of the circle squared must then be applied to square root and then the measure for the radius of the circle can then be known. Remember to reduce the decimal places to 2 or 3 or 4 digits if the result involves an infinite amount of decimal places. Also if the desire is to have the result read as a whole number 0.1 can be added to a value that is reduced to 3 decimal digits and ends in 0.99. Remember that the radius of a circle is half of the diameter of a circle.
“Using Pi to find the surface area of a Sphere”:
Pi can also be used to find the surface area of a Sphere. A sphere is a 3-dimensional version of a circle. A circle is 2-dimensional.
To find the surface area of Sphere first create a circle with the same diameter of measure as the Sphere and then discover the area of that circle and the surface are of a Sphere is 4 times larger than the area of a circle with a diameter of equal measure to the diameter of the Sphere.
Alternatively the surface area of a Sphere can be found with the following steps:
1. Know the parts of the equation, Surface Area = 4πr2. ...
2. Find the radius of the sphere. ...
3. Square the radius by multiplying it by itself. ...
4. Multiply this result by 4. ...
5. Multiply the results by pi (π). ...
6. Remember to add your units to the final answer. ...
7. Practice with an example. ...
Understand surface area.
“Using Pi to find the volume of a Sphere”:
“The volume of a Sphere can also be found by involving Pi in the equation” by following the steps proceeding”:
1.Write down the equation for calculating the volume of a sphere. This is the equation: V = ⁴⁄₃πr³. ...
2.Find the radius. If you're given the radius, then you can move on to the next step. ...
3.Cube the radius. ...
4.Multiply the cubed radius by 4/3. ...
5.Multiply the equation by π.
>
Subject | Views | Written By | Posted |
---|---|---|---|
The Megalithic Yard Defined Simply | 385 | Ahatmose | 03-Jan-11 16:13 |
Re: The Megalithic Yard Defined Simply | 51 | magisterchessmutt | 03-Jan-11 23:51 |
Re: The Megalithic Yard Defined Simply | 53 | Ahatmose | 04-Jan-11 04:38 |
Re: The Megalithic Yard Defined Simply | 63 | Ahatmose | 04-Jan-11 04:40 |
Re: The Megalithic Yard Defined Simply | 185 | Liddz | 21-Apr-17 15:52 |
Finding The Circumference Without Knowing Pi!!! | 48 | Ahatmose | 04-Jan-11 14:57 |
Re: The Megalithic Yard Defined Simply | 55 | Ahatmose | 04-Jan-11 04:59 |
Re: The Megalithic Yard Defined Simply | 76 | Glanymor1948 | 04-Jan-11 12:57 |
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