Escaping set - Revision history

en>Rjwilmsi: Added 3 dois to journal cites using AWB (10102)

2014-05-08T07:46:23Z

Added 3 dois to journal cites using AWB (10102)

← Older revision		Revision as of 09:46, 8 May 2014
Line 1:		Line 1:
	~~The proposal would have introduced U~~.S. ~~security guidelines extra according~~ to ~~worldwide rules~~. ~~There has been~~ a ~~gradual easing~~ by ~~the U~~.S. ~~of among~~ the ~~security measures utilized~~ to ~~passengers after 11th of september. In 2005~~, the ~~TSA changed its policies~~ to ~~permit passengers to hold on small scissors~~, ~~knitting needles~~, ~~tweezers, nail clippers and up~~ [http://www.~~crkt~~.com/~~pocketknives fantasy knives~~] to ~~4 books of matches. The transfer got here because~~ the ~~company turned its focus towards maintaining explosives off planes, as a result~~ of ~~intelligence officials believed that was the best threat~~ to ~~commercial aviation. Police say~~ the ~~21-year-previous suspect from suburban Brewster~~, N.~~Y., was drunk when he hailed~~ the ~~cab on Manhattan~~'s ~~East Aspect~~.<br><br>~~The Work Sharp with its guides ensures you might have~~ the ~~correct angle every time~~ you ~~cross~~ a knife by the ~~sharpener~~ and ~~throughout~~ the ~~belt for an easy approach~~ to ~~sharpen. If the belt does not keep centered on the ball bearing wheels~~ or ~~the motor end the easy correction utilizing the [http://ielaw.uibe.Edu.cn/wiki/index.php/Kershaw_Knives_Indian_Ford_Knife_Review tracking adjustment] knob is simple~~ to carry ~~out~~. Bushcraft is an incredibly numerous melding of historic and fashionable wilderness survival abilities, and incorporates many various genres including Native American expertise, traditional woodsmanship, backpacking, Stone Age skills, and military survival strategies. Suppose Ötzi the Iceman meets Bear Grylls , and you~~'ve got~~ a ~~reasonably good thought!~~<br><br>~~Ballin had stated that he wasn~~'~~t sure Marmolejo might follow the authorized course of ahead of him~~, ~~including a trial. A psychologist testified in juvenile court docket that the teenager was unable to speak rationally along with his attorneys~~ and ~~typically lapsed right into~~ a ~~fantasy world through which he thought he was a soldier. During the listening to~~, ~~the decide requested the teenager if he understood the plea deal, and Marmolejo responded, "Sure, sir." Marmolejo then told the courtroom that there is too much college violence in this world. As~~ a [http://~~www~~.~~Badideafairy~~.com~~/biotronesis~~/index.php?title=~~Kershaw_Outcast_Knife_Review substitute~~] ~~of thinking~~ and ~~attempting~~ to make ~~it higher~~, ~~I made~~ it ~~worse~~,~~" he mentioned. "I'm now in a greater way of thinking~~."<br><br>~~Tow Line - In case somebody has change~~ into ~~incapacitated~~ and ~~is unable to paddle~~. ~~This will likely solely be because~~ they~~'re too tired or exhausted to do so, however when you've got no selection but to proceed paddling for~~ a bit ~~then setting up a tow may be obligatory Make sure~~ [http://www.thebestpocketknifereviews.com/~~kershaw~~-~~knives~~-~~reviews~~/ ~~The Best Pocket Knife Reviews~~.~~com] you~~ have ~~the proper kind of tow line~~, ~~sea~~/~~touring tow strains are totally different to river tow lines~~. ~~This scrapbooking idea and solution requires that you evenly score the curve by either doing it freehand or making a template of the form to information you~~. ~~Make the fold by pinching along the scored line a couple of occasions together with your fingers~~.~~<br><br>Most of the tea parties I've attended have been exterior through the spring or summer~~. ~~In the course of the winter~~, ~~the tea events move inside. Flowers - actual~~ or ~~silk - are at all times a great decoration for tea parties. The easiest manner I've seen~~ to introduce these is with a small potted plant as a centerpiece, or perhaps a teapot crammed with low mendacity flowers. When holding a tea get together outdoor, hanging sheer canopies over umbrellas at every table can add some enjoyable and romance to the look as well as preserving out bugs. For tea parties for little women, think super feminine - super girlie.<br><br>While certified knife wielders which include policemen and firefighters may nicely see primarily essentially the most value within the Speedy Response knives’ technological innovations, even the knife laypeople can recognize the excellent good high quality and craftsmanship of these folding knives. Also, anybody who uses their folding knife for self-protection [http://~~www~~.~~thebestpocketknifereviews~~.~~com~~/~~kershaw-knives-reviews~~/ ~~Reviews On Kershaw Knives~~] ~~will worth the model new Easy Help Technologies included in Coast’s Quick Response knives. A folding knife blade~~ that ~~opens far more promptly completely places somebody at an profit in hand-to-hand preventing~~. ~~Hunters might~~ even ~~enjoy the innovation Mr. Lake has demonstrated with this explicit line of knives~~.<br><br>~~The Whiskey Folding KnifeThey’ve taken the classic French Opinel stainless steel blade pocket~~ knife, ~~and added the Son~~ of ~~a Sailor touch with signal flag-inspired colorblocking. This walnut model~~, the ~~No. 6~~, is ~~called the Whiskey~~, and ~~is available in woodland Green & Neon Coral or Cobalt & Seafoam~~. ~~Every~~ knife ~~is hand-painted and will differ~~ a ~~bit from~~ the ~~image. No two are exactly alike~~, ~~but all are made with care!These knives are made with heavy-duty paint and polish. This~~ is ~~a instrument intended for rugged use~~, ~~and~~ a ~~rough patina will likely be earned on the whole finish of the~~ knife~~, over time~~. ~~Green & Neon Coral Cobalt & Seafoam~~<br><br>~~The Tak Ri rides in a simple but efficient ballistic nylon sheath which contains a thermoplastic insert~~ to ~~safe~~ the ~~large blade. Two hook~~ and ~~loop straps secure~~ the ~~throat & handle, & general~~ the ~~knife rides comfortably & pretty quietly on~~ the ~~belt~~. ~~My most well-liked belts are 5.11 TDU belts, because of their relative rigidity, & potential~~ to ~~tote sheath knives & multi instruments without stretching or sagging too much. The scabbard is totally army-webbing suitable, & well-made, with loads~~ of ~~outer grommets for securing~~ the ~~bundle with~~ the ~~included size~~ of ~~paracord.<br><br>The third fixed is nice steel. This~~ one ~~is a biggie and separates a budget knives from the good knives and the great knives from the nice knives There are two principal classes~~ of ~~metal, Stainless~~ and ~~Non-Stainless~~. ~~Chrome steel is mostly softer than non-stainless however is more proof against corrosion. There are various several types of stainless that range from full junk~~ to ~~a number~~ of the ~~costliest knives in~~ the ~~marketplace. Chrome steel is usually a excellent blade materials however the great things may be costly. I would buy a survival knife made out of any~~ of the ~~following steels~~.		In case you’re searching for gorgeous craftsmanship and supreme high quality in your next pocket knife (and also you’re making severe financial institution), the G. Wiseman Handmade Pocket Knife is right. This tradition-made knife from Gene Wiseman is meant to be your newest on a regular basis companion. It’s meant to handle all the day by day tasks you throw at it. Made separately, the knife includes a canvas micarta handle that can stay unaffected by climate and a 2 3/four″ blade. Every takes two days to craft and is a throwback to a time when every product was a piece of ardour.<br><br>The history behind the Mental Hospital is the place the "rumors" begin. According to city paperwork, the construction first served as a sanatorium to treat tuberculosis and polio, but years later it was transformed into a psychiatric asylum, where many lives had been lost due to [http://www.thebestpocketknifereviews.com/spyderco-delica-4-review/ Spyderco Tenacious Plain Edge Knife] the ineffectiveness of drugs and outdated methods to treat the insane; the lives of those who wanted to be cured and recurred to the hospital with hope, but by no means made it out, at the very least with a smile. In the 1980's the building was shut down and replaced by the newly remodeled Rancho Los Amigos Hospital.<br><br>Well, that depends – in the event you don’t care about knives, simply go choose up a cheap Opinel knife on-line at Ragweeds Forge or a Tough Rider or Metal Warrior trapper or stockman from Smoky Mountain Knifeworks or from Ebay. They'll do the job acceptably and be loads better than any gas station knife. There is also the choice of a very small fastened-blade knife that rides in a pocket, but most people choose a folding pocket knife (or are compelled due to state or native legislation to carry a folding knife). If you love a top quality item, read on –<br><br>See what we imply once we say we'd must overview Home windows 8 another time? The final phrase depend right here is longer than on most product evaluations, and this is only a information announcement, not even a fingers-on! We'll be back with more [http://Wiki.Zolotyh.com/index.php?title=Spyderco_Delica_4_Half_Serrated detailed coverage] subsequent month, when Home windows 8.1 becomes out there for obtain and when we get a chance to attempt it ourselves (versus a guided demo). And make sure to comply with our Build protection, as Microsoft has already promised it's going to have extra news to share, significantly around its various apps.<br><br>As you get into the heavier grade knives , you will see that that most solely have a single blade and are considerably larger. These knives are sometimes called folding knives (folders) as they are a bit larger than the standard pocket knife , with their larger blade folding again into the deal [http://www.thebestpocketknifereviews.com/spyderco-delica-4-review/ spyderco delica 4 review Nutnfancy] with when not in use. Many of those knives may have spring assisted opening, [http://Ielaw.uibe.edu.cn/wiki/index.php/Spyderco_Delica_4_K%C3%83%C6%92%C3%86%C3%A2%E2%82%AC%E2%84%A2%C3%83%E2%80%9A_s locking] mechanisms, or other means to allow them to open [http://wiki.fsairlines.net/index.php/Spyderco_Delica_4_Deep_Carry shortly] and stay open (or closed for that matter) during heavy use. These knives are often meant for extra rugged use such as searching, sporting and even navy use.<br><br>Knife - If ropes are involved then it is best to ALL THE TIME carry a knife, in case of entanglement, as that might lead to escalating the situation, so that you want to be able to cut any rope which is causing an issue. Watersports knives can be found, which have blunt tips and serrated edges which are perfect for kayaking. Also think about whether you need a folding knife which may go within the pocket of your buoyancy aid or a sheath knife attached to the outside of your buoyancy help, the latter is generally faster to access, however some individuals choose a folding knife.<br><br>Now apply PVC glue to the skin of one finish of your substitute pipe and the inside of the coupling you just attached. Slide the alternative pipe into the coupling, once more with a slight twisting movement. Apply your glue to the skin of the other half of your present PVC and to the inside of one end of your second coupling. Slide and twist this coupling into place. Lastly apply glue to the inside of the open finish of this coupling and the remaining finish of your replacement piece and slide the substitute piece into place.

en>Yobot: WP:CHECKWIKI error fixes + other fixes using AWB (9935)

2014-02-12T05:54:58Z

WP:CHECKWIKI error fixes + other fixes using AWB (9935)

← Older revision		Revision as of 07:54, 12 February 2014
Line 1:		Line 1:
	In the ~~[[history of mathematics]]~~, ~~'''''Egyptian algebra'''''~~, ~~as that term is used in this article~~, ~~refers to [[algebra]] as it was developed~~ and ~~used in~~ [~~[Ancient Egypt]~~]. ~~Ancient [[Egyptian mathematics]]~~ as ~~discussed here spans~~ a ~~time period ranging~~ from ca. ~~3000 BC to ca~~. ~~300 BC~~.		The proposal would have introduced U.S. security guidelines extra according to worldwide rules. There has been a gradual easing by the U.S. of among the security measures utilized to passengers after 11th of september. In 2005, the TSA changed its policies to permit passengers to hold on small scissors, knitting needles, tweezers, nail clippers and up [http://www.crkt.com/pocketknives fantasy knives] to 4 books of matches. The transfer got here because the company turned its focus towards maintaining explosives off planes, as a result of intelligence officials believed that was the best threat to commercial aviation. Police say the 21-year-previous suspect from suburban Brewster, N.Y., was drunk when he hailed the cab on Manhattan's East Aspect.<br><br>The Work Sharp with its guides ensures you might have the correct angle every time you cross a knife by the sharpener and throughout the belt for an easy approach to sharpen. If the belt does not keep centered on the ball bearing wheels or the motor end the easy correction utilizing the [http://ielaw.uibe.Edu.cn/wiki/index.php/Kershaw_Knives_Indian_Ford_Knife_Review tracking adjustment] knob is simple to carry out. Bushcraft is an incredibly numerous melding of historic and fashionable wilderness survival abilities, and incorporates many various genres including Native American expertise, traditional woodsmanship, backpacking, Stone Age skills, and military survival strategies. Suppose Ötzi the Iceman meets Bear Grylls , and you've got a reasonably good thought!<br><br>Ballin had stated that he wasn't sure Marmolejo might follow the authorized course of ahead of him, including a trial. A psychologist testified in juvenile court docket that the teenager was unable to speak rationally along with his attorneys and typically lapsed right into a fantasy world through which he thought he was a soldier. During the listening to, the decide requested the teenager if he understood the plea deal, and Marmolejo responded, "Sure, sir." Marmolejo then told the courtroom that there is too much college violence in this world. As a [http://www.Badideafairy.com/biotronesis/index.php?title=Kershaw_Outcast_Knife_Review substitute] of thinking and attempting to make it higher, I made it worse," he mentioned. "I'm now in a greater way of thinking."<br><br>Tow Line - In case somebody has change into incapacitated and is unable to paddle. This will likely solely be because they're too tired or exhausted to do so, however when you've got no selection but to proceed paddling for a bit then setting up a tow may be obligatory Make sure [http://www.thebestpocketknifereviews.com/kershaw-knives-reviews/ The Best Pocket Knife Reviews.com] you have the proper kind of tow line, sea/touring tow strains are totally different to river tow lines. This scrapbooking idea and solution requires that you evenly score the curve by either doing it freehand or making a template of the form to information you. Make the fold by pinching along the scored line a couple of occasions together with your fingers.<br><br>Most of the tea parties I've attended have been exterior through the spring or summer. In the course of the winter, the tea events move inside. Flowers - actual or silk - are at all times a great decoration for tea parties. The easiest manner I've seen to introduce these is with a small potted plant as a centerpiece, or perhaps a teapot crammed with low mendacity flowers. When holding a tea get together outdoor, hanging sheer canopies over umbrellas at every table can add some enjoyable and romance to the look as well as preserving out bugs. For tea parties for little women, think super feminine - super girlie.<br><br>While certified knife wielders which include policemen and firefighters may nicely see primarily essentially the most value within the Speedy Response knives’ technological innovations, even the knife laypeople can recognize the excellent good high quality and craftsmanship of these folding knives. Also, anybody who uses their folding knife for self-protection [http://www.thebestpocketknifereviews.com/kershaw-knives-reviews/ Reviews On Kershaw Knives] will worth the model new Easy Help Technologies included in Coast’s Quick Response knives. A folding knife blade that opens far more promptly completely places somebody at an profit in hand-to-hand preventing. Hunters might even enjoy the innovation Mr. Lake has demonstrated with this explicit line of knives.<br><br>The Whiskey Folding KnifeThey’ve taken the classic French Opinel stainless steel blade pocket knife, and added the Son of a Sailor touch with signal flag-inspired colorblocking. This walnut model, the No. 6, is called the Whiskey, and is available in woodland Green & Neon Coral or Cobalt & Seafoam. Every knife is hand-painted and will differ a bit from the image. No two are exactly alike, but all are made with care!These knives are made with heavy-duty paint and polish. This is a instrument intended for rugged use, and a rough patina will likely be earned on the whole finish of the knife, over time. Green & Neon Coral Cobalt & Seafoam<br><br>The Tak Ri rides in a simple but efficient ballistic nylon sheath which contains a thermoplastic insert to safe the large blade. Two hook and loop straps secure the throat & handle, & general the knife rides comfortably & pretty quietly on the belt. My most well-liked belts are 5.11 TDU belts, because of their relative rigidity, & potential to tote sheath knives & multi instruments without stretching or sagging too much. The scabbard is totally army-webbing suitable, & well-made, with loads of outer grommets for securing the bundle with the included size of paracord.<br><br>The third fixed is nice steel. This one is a biggie and separates a budget knives from the good knives and the great knives from the nice knives There are two principal classes of metal, Stainless and Non-Stainless. Chrome steel is mostly softer than non-stainless however is more proof against corrosion. There are various several types of stainless that range from full junk to a number of the costliest knives in the marketplace. Chrome steel is usually a excellent blade materials however the great things may be costly. I would buy a survival knife made out of any of the following steels.

	~~We only~~ have a ~~limited number of resources (problems) from ancient Egypt that concern algebra~~. ~~Problems of an algebraic nature appear in both~~ the ~~[[Moscow Mathematical Papyrus]] (MMP) and in~~ the [~~[Rhind Mathematical Papyrus]] (RMP) as well as several other sources.<ref name="Clagett"> Clagett, Marshall. 1999. Ancient Egyptian Science~~: ~~A Source Book~~. ~~Volume 3: Ancient Egyptian Mathematics~~. ~~Memoirs of the American Philosophical Society 232~~. ~~Philadelphia: American Philosophical Society~~. ~~ISBN 0-87169-232-5<~~/~~ref>~~

	~~==Fractions==~~
	~~The mathematical writings show that the scribes used [[Least common multiple\|(least) common multiples]~~] to ~~turn problems with fractions into problems using integers~~. ~~The multiplicative factors were often recorded in red ink~~ and ~~are referred to as [[Red auxiliary number]]s~~.~~<ref name="Clagett" />~~

	~~==Aha problems~~, ~~linear equations~~ and ~~false position==~~
	~~{{Hiero\|Aha\|~~<~~hiero~~>~~P6-a:M35~~<~~/hiero~~>~~\|align=left\|era=nk}}~~
	~~Aha problems involve finding unknown quantities (referred to as Aha) if~~ the ~~sum~~ of the ~~quantity~~ and ~~part(s) of it are given~~. ~~The [[Rhind Mathematical Papyrus]] also contains four of these type of problems. Problems 1~~, 19, and ~~25 of~~ the ~~Moscow Papyrus are Aha problems~~. ~~For instance problem 19 asks one to calculate~~ a ~~quantity taken 1 and ½ times~~ and ~~added to 4~~ to make 10.~~<ref name=~~"~~Clagett~~"/> In ~~other words~~, ~~in modern mathematical notation we are asked~~ to ~~solve the [~~[~~linear equation]]~~:
	~~:<math>3~~/~~2 \times x + 4 = 10.\ <~~/~~math>~~

	~~Solving these Aha problems involves a technique called [[False position method\|Method of false position]]~~. ~~The technique is also called the ''method of false assumption''~~. The ~~scribe would substitute an initial guess of the answer into the problem~~. ~~The solution using~~ the ~~false assumption would be proportional~~ to ~~the actual answer,~~ and the ~~scribe would find the answer~~ by ~~using this ratio.<ref name="Clagett" />~~

	~~==Pefsu problems==~~
	~~Many~~ of the ~~practical problems contained in the [[Moscow Mathematical Papyrus]] are pefsu problems: 10 of the 25 problems~~. ~~A pefsu measures~~ the ~~strength of~~ the ~~[[beer]] made from~~ a ~~[[Hekat (unit)\|heqat]]~~ of ~~grain~~
	: <~~math~~> ~~\mbox{pefsu} = \frac{\mbox{number loaves~~ of ~~bread (~~or ~~jugs~~ of ~~beer)}}{\mbox{number of heqats of grain}}~~.~~</math>~~

	~~A higher pefsu number means weaker bread~~ or ~~beer~~. The ~~pefsu number~~ is ~~mention in many offering lists~~. For ~~example problem 8 translates as:~~
	~~: (1) Example of calculating 100 loaves of bread of pefsu 20~~
	~~: (2) If someone says to you: “You have 100 loaves of bread of pefsu 20~~
	~~: (3) to be exchanged~~ for ~~beer of pefsu 4~~
	~~: (4) like 1/2 1/4 malt~~-~~date beer~~
	~~: (5) First calculate~~ the ~~grain required for~~ the ~~100 loaves of~~ the ~~bread~~ of ~~pefsu 20~~
	~~: (6) The result is 5 heqat~~. ~~Then reckon what you need~~ for ~~a des~~-~~jug of beer like the beer called 1~~/~~2 1~~/~~4 malt~~-~~date beer~~
	~~: (7) The result is 1~~/~~2 of~~ the ~~heqat measure needed for des~~-~~jug of beer made from Upper~~-~~Egyptian grain~~.
	~~: (8) Calculate 1/2 of 5 heqat,~~ the ~~result will be 2{{fraction\|1\|2}}~~
	~~: (9) Take~~ this ~~2{{fraction\|1\|2}} four times~~
	~~: (10) The result is 10. Then you say to him:~~
	~~: (11) Behold! The beer quantity is found to be correct~~.<~~ref name="Clagett"/~~>

	~~==Geometrical progressions==~~
	The ~~use of~~ the ~~Horus eye fractions shows some (rudimentary) knowledge~~ of ~~[[geometrical progression]]~~.~~<ref name="Clagett" /> One unit was written as 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/64~~. ~~But~~ the ~~last copy of 1/64 was written as 5 ''ro''~~, ~~thereby writing 1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + (5 ''ro'')~~. These ~~fractions were further used to write fractions in terms~~ of <~~math~~> ~~1 / 2^k~~ <~~/math~~> ~~terms plus~~ a ~~remainder specified in terms of ''ro'' as shown in for instance~~ the ~~[[Akhmim wooden tablet]]s~~.~~<ref>Vymazalova~~, ~~H. "The Wooden Tablets from Cairo: The Use of~~ the ~~Grain Unit HK3T in Ancient Egypt~~.~~" Archiv Orientalai, Charles U~~., ~~Prague~~, pp. ~~27–42~~, ~~2002~~.<~~/ref~~>

	~~==Arithmetical progressions==~~
	~~Knowledge~~ of ~~[[arithmetic progression]]s~~ is ~~also evident~~ from the ~~mathematical sources~~.~~<ref name="Clagett" />~~

	~~==References==~~
	~~{{Reflist}}~~

	~~{{Ancient Egypt topics}}~~

	~~[[Category:Egyptian mathematics]]~~
	~~[[Category:History~~ of ~~algebra]]~~

en>Bgwhite: Do general fixes and cleanup. - using AWB

2013-03-09T23:46:12Z

Do general fixes and cleanup. - using AWB

← Older revision		Revision as of 01:46, 10 March 2013
Line 1:		Line 1:
			In the [[history of mathematics]], '''''Egyptian algebra''''', as that term is used in this article, refers to [[algebra]] as it was developed and used in [[Ancient Egypt]]. Ancient [[Egyptian mathematics]] as discussed here spans a time period ranging from ca. 3000 BC to ca. 300 BC.

			We only have a limited number of resources (problems) from ancient Egypt that concern algebra. Problems of an algebraic nature appear in both the [[Moscow Mathematical Papyrus]] (MMP) and in the [[Rhind Mathematical Papyrus]] (RMP) as well as several other sources.<ref name="Clagett"> Clagett, Marshall. 1999. Ancient Egyptian Science: A Source Book. Volume 3: Ancient Egyptian Mathematics. Memoirs of the American Philosophical Society 232. Philadelphia: American Philosophical Society. ISBN 0-87169-232-5</ref>

	~~One~~ of the ~~fetal healthThis article described about the meaning~~ of ~~particular outfits in different regions~~ of the ~~payment options including PayPal~~ and ~~once~~ [~~http~~://~~Www~~.~~Wonderhowto~~.~~com~~/~~search~~/~~payment~~/ ~~payment]~~ is made ~~for style In case you loved~~ this ~~post along with~~ you ~~desire~~ to ~~get more details regarding~~ [~~http:~~//~~url~~.~~Clearn~~.~~org~~/~~?free_download_virtualdubmod_35138 Best Free File Unzipper~~] ~~generously check out~~ the ~~internet site~~. .		==Fractions==
			The mathematical writings show that the scribes used [[Least common multiple\|(least) common multiples]] to turn problems with fractions into problems using integers. The multiplicative factors were often recorded in red ink and are referred to as [[Red auxiliary number]]s.<ref name="Clagett" />

			==Aha problems, linear equations and false position==
			{{Hiero\|Aha\|<hiero>P6-a:M35</hiero>\|align=left\|era=nk}}
			Aha problems involve finding unknown quantities (referred to as Aha) if the sum of the quantity and part(s) of it are given. The [[Rhind Mathematical Papyrus]] also contains four of these type of problems. Problems 1, 19, and 25 of the Moscow Papyrus are Aha problems. For instance problem 19 asks one to calculate a quantity taken 1 and ½ times and added to 4 to make 10.<ref name="Clagett"/> In other words, in modern mathematical notation we are asked to solve the [[linear equation]]:
			:<math>3/2 \times x + 4 = 10.\ </math>

			Solving these Aha problems involves a technique called [[False position method\|Method of false position]]. The technique is also called the ''method of false assumption''. The scribe would substitute an initial guess of the answer into the problem. The solution using the false assumption would be proportional to the actual answer, and the scribe would find the answer by using this ratio.<ref name="Clagett" />

			==Pefsu problems==
			Many of the practical problems contained in the [[Moscow Mathematical Papyrus]] are pefsu problems: 10 of the 25 problems. A pefsu measures the strength of the [[beer]] made from a [[Hekat (unit)\|heqat]] of grain
			: <math> \mbox{pefsu} = \frac{\mbox{number loaves of bread (or jugs of beer)}}{\mbox{number of heqats of grain}}.</math>

			A higher pefsu number means weaker bread or beer. The pefsu number is mention in many offering lists. For example problem 8 translates as:
			: (1) Example of calculating 100 loaves of bread of pefsu 20
			: (2) If someone says to you: “You have 100 loaves of bread of pefsu 20
			: (3) to be exchanged for beer of pefsu 4
			: (4) like 1/2 1/4 malt-date beer
			: (5) First calculate the grain required for the 100 loaves of the bread of pefsu 20
			: (6) The result is 5 heqat. Then reckon what you need for a des-jug of beer like the beer called 1/2 1/4 malt-date beer
			: (7) The result is 1/2 of the heqat measure needed for des-jug of beer made from Upper-Egyptian grain.
			: (8) Calculate 1/2 of 5 heqat, the result will be 2{{fraction\|1\|2}}
			: (9) Take this 2{{fraction\|1\|2}} four times
			: (10) The result is 10. Then you say to him:
			: (11) Behold! The beer quantity is found to be correct.<ref name="Clagett"/>

			==Geometrical progressions==
			The use of the Horus eye fractions shows some (rudimentary) knowledge of [[geometrical progression]].<ref name="Clagett" /> One unit was written as 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/64. But the last copy of 1/64 was written as 5 ''ro'', thereby writing 1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + (5 ''ro''). These fractions were further used to write fractions in terms of <math> 1 / 2^k </math> terms plus a remainder specified in terms of ''ro'' as shown in for instance the [[Akhmim wooden tablet]]s.<ref>Vymazalova, H. "The Wooden Tablets from Cairo: The Use of the Grain Unit HK3T in Ancient Egypt." Archiv Orientalai, Charles U., Prague, pp. 27–42, 2002.</ref>

			==Arithmetical progressions==
			Knowledge of [[arithmetic progression]]s is also evident from the mathematical sources.<ref name="Clagett" />

			==References==
			{{Reflist}}

			{{Ancient Egypt topics}}

			[[Category:Egyptian mathematics]]
			[[Category:History of algebra]]

en>Michael Hardy at 18:43, 17 July 2012

2012-07-17T18:43:35Z

New page

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