tag:blogger.com,1999:blog-27865295.post114726532343598009..comments2014-05-28T13:56:32.767-07:00Comments on History of Egyptian Fractions: Egyptian Fractionsmilo gardnernoreply@blogger.comBlogger4125tag:blogger.com,1999:blog-27865295.post-77913673724817868902014-05-28T13:56:32.767-07:002014-05-28T13:56:32.767-07:00Moscow Mathematical Papyrus
.
Moscow Mathemati...Moscow Mathematical Papyrus<br /><br /><br /> .<br /><br />Moscow Mathematical Papyrus<br /><br /><br /><br /><br /><br /><br />The Moscow Mathematical Papyrus (MMP),also known as the Golenischev Mathematical Papyrus, was once owned by Egyptologist Vladimir Golenidenov. Today the document is housed in the Pushkin State Museum of Fine Arts in Moscow. Based on the palaeography of the hieratic text dates to the Eleventh dynasty of Egypt. Approximately 18 feet long and varying between 1 1/2 and 3 inches wide, its format was divided into 25 problems with tentative solutions by the Soviet Orientalist Vasily Vasilievich Struve in 1930. It is one of a half dozen well-known Mathematical Papyri. Along with the Rhind Mathematical Papyrus(RMP), the Kahun Papyrus(KP), the Berlin Papyrus (KP), the Egyptian Mathematical Papyrus (EMLR), the Akhmim Wooden TabletPlanetmathPlanetmath(AWT), and the Ebers Papyrus(EB). The MMP is about the same age as the AWT, BP, KP, and the EMLR, and about 250 years older than the RMP and EB.<br /><br /><br />The 10th problems of the MMP calculated the area of a hemisphere, a 1/2 slice of a cylinder. Gillings dedicated a chapter to a diameter (D/2) times (D/2) times pi = 256/81 as the area of a circle, cubit x cubit, a topic repeated in RMP 41,42, 43, 44, 45, and 46 by adding height to compute volume, cubit x cubit x cubit.<br /><br /><br />The MMP began with the modern area of the circle<br /><br /> <br />A=(pi)r 2 <br /> <br /><br />and replaced pi with 256/81 and r with D/2 and considered:<br /><br /><br />1. A = (256/81)(D/2)(D/2) 2. A = (64/81)(D)(D) 3. A = (8/9)(8/9)(D)(D)<br /><br /><br />The scribe input D = 9 and found the area of a semi-circle<br /><br /><br />4. A = ((9 - 9/9) = [(8)(8)]/2 = 64/2 = 32 (the cubit squared unit was omitted)<br /><br /><br />in RMP 41 Ahmes input D = 9<br /><br /><br />5. A = (9 - 9/9) = (8)(8) = 64 cubits squared<br /><br /><br />In RMP 42 Ahmes input D = 10<br /><br /><br />6. A = (10 - 10/9) = (80/9)(80/9) = 6400/81 = (79 + 1/81)cubits squared<br /><br /><br />and input H =10<br /><br /><br />7. V = (6400/81)(10) = 64000/81 = 790 + 10/81 = 790 + 20/162 = [790 + (18 + 2)/162 = 790 + 1/18 + 1/81]<br /><br /><br />and converted to khar units by:<br /><br /><br />8. V = [790 +10/81] + 1/2[790 + 10/81] = [1185 + 15/81]khar<br /><br /><br />leaving rational numberPlanetmathPlanetmathPlanetmath conversions to unit fraction series calculations to the reader.<br /><br /><br />milo gardnerhttps://www.blogger.com/profile/00681791752558320299noreply@blogger.comtag:blogger.com,1999:blog-27865295.post-13637987313651641582014-03-12T13:03:56.441-07:002014-03-12T13:03:56.441-07:00I have just been looking at property in sharm el s...I have just been looking at <a href="http://www.azureoverseas.com/egypt/sharm-el-sheikh/" rel="nofollow">property in sharm el shake</a>, This was helpful thank you<br /> ste tomkinsonhttps://www.blogger.com/profile/05508492533937104574noreply@blogger.comtag:blogger.com,1999:blog-27865295.post-6762321293931678982010-10-05T23:58:20.815-07:002010-10-05T23:58:20.815-07:00This is very interesting stuff. Our bigoted, schoo...This is very interesting stuff. Our bigoted, school boyish view needs to be updated. It was good enough to go out and conquer an empire, but will not do today, when we know much more about indigenous peoples and there cultures.samhttps://www.blogger.com/profile/13285732655305958008noreply@blogger.comtag:blogger.com,1999:blog-27865295.post-21769958659516456552007-04-18T23:06:00.000-07:002007-04-18T23:06:00.000-07:00This comment has been removed by a blog administrator.Ayishahttps://www.blogger.com/profile/14790237594110917232noreply@blogger.com