1
Imphal Times Supplementary issue Page No. 2 Letters, Feedback and Suggestions to ‘Imphal Times’ can be sent to our e-mail : [email protected]. For advertisement kindy contact: - 0385-2452159 (O). For time being readers can reach the office at Cell Phone No. 9862860745 for any purpose. Friday, August 2, 2019 Editorial Courtesy The Wire By : Kamala Ganesh She has a visible presence in Chennai; her statue stands in the premises of the Cancer Institute at Adyar, a leading centre for oncology in the country. The road leading to Besant Nagar from Adyar bridge is named after her. Yesterday, the Tamil Nadu government announced that her birthday would be celebrated every year as ‘Hospital Day’. For the millennials and post- millennials in the city, however, Dr. Muthulakshmi Reddi is a hazy, hearsay figure of the nationalist era – feisty and articulate, but as to what exactly about, they would have to scratch their heads and think. On the other hand, the older generation of politically aware denizens of Tamil Nadu know about her accomplishments, but mostly as a chronological narrative of positions held and organisations established. From the vantage point of hindsight, I think there is no doubt that Muthulakshmi was a powerful face of nationalist feminism in the first half of the 20 th century, with all the complexities that this entailed. Her voluminous speeches and writings are indeed ideologically driven, with elements from the discourses of social reform and nationalism combined with empathy for the issues espoused by the Justice Party and a bent towards international feminism. But it is in her concrete actions, specifically in establishing the Avvai Home in 1932 for destitute and abandoned girls and women, and the Cancer Institute under the aegis of the Women’s Indian Association (WIA) in 1952 that we see the unique nature of her contribution. The protocols and ethos she created in these institutions are exemplars of an ethic of care, inspired both by feminism and Gandhian nationalism. But more on this later. Born in Pudukkottai to Chandramma, a former devadasi and Narayanaswami Iyer, principal of the Maharaja college, Muthulakshmi had to surmount huge obstacles created by her gender and caste, and struggle to get an education. In 1912, she became the first woman medical graduate from the Madras Presidency; she went on to become an obstetrician. In an interview in 2010, Sarojini Varadappan, a renowned social worker who worked closely with Muthulakshmi, remembers her as an impressive, even formidable, personality. Immaculately dressed in heavy Kanjeevaram saris pinned with a brooch, and shining diamond earrings, Muthulakshmi had a flourishing practice delivering the babies of all the rich Mylapore professionals. Influenced by the women’s movement and the national movement, Muthulakshmi turned her attention to politics and public life. From 1926 to 1930, she was a member of the legislative council in British India, the first woman to be so nominated. She became the first woman in the world to become the Deputy President of a legislative council. As a legislator she was an indefatigable campaigner and lobbyist for women’s rights on a range of issues, including medical inspection in girls’ schools, exemption from school fees for poor girls, maternity and child welfare, and reservation for women in various structures of civic administration. She was closely associated with the All Dr. Muthulakshmi Reddi: A Powerful Face of Nationalist Feminism India Women’s Conference and the Women’s India Association. She edited the multilingual quarterly journal, Stree Dharma, started in 1918. Most notably, Muthulakshmi brought in legislation to abolish the devadasi system and child marriage. This campaign triggered stiff opposition from Congress stalwarts like Rajaji and S. Satyamurthi. When Satyamurthi argued in the Legislative Council that the devadasi system was an ancient religious custom, with devadasis being the custodians of the traditional arts, she famously retorted that if such a caste was indeed necessary and since the devadasis had done it for so long, why did the Brahmin women not take over? Muthulakshmi would not have imagined that decades later she would be criticised by contemporary feminists and her campaign would be seen as a patronising gesture. Sociologist Amrit Srinivasan’s 1985 article, ‘Reform and Revival: The devadasi and her dance’, was followed by much writing on the devadasis, their original putative respected social status and their later ‘fall’, and the loss for the classical performing arts traditions of South India. In particular, Muthulakshmi’s campaign was criticised as it was perceived as disenfranchising devadasis from traditional privileges and denying them subjecthood and agency. Historian S. Anandi, while lauding her undeniable commitment to women’s rights, sees her as ‘othering’ devadasis and moralising on their liberation from the clutches of the system as the only way out. But look at it from Muthulakshmi’s perspective. Given the humiliations she underwent, unsurprisingly she saw the devadasi system as a social evil. In fact, one could infer that to a large extent, her personal anger was what gave her campaign its sharp edge. Modern education was, for her, the answer again understandable given her own achievements in her profession and in public service. The sincerity of her efforts to improve the situation of devadasi women is undeniable. Her tone inevitably echoed that of the entire social reform movement in that era, warts and all; it did not eclipse the basic drive for emancipation and equality. In fact, Avvai Home and Orphanage, that venerable institution established by Muthulakshmi in 1931, started spontaneously when three girls from Namakkal, from devadasi families, arrived unannounced at her doorstep one night. They had run away from home with nowhere to go. Immediately she took them into her own home and that became Avvai Home, later shifting to its own premises. It has since expanded to include a school and also a teacher’s training school, and is one of the early and enduring examples of formalising the ethic of care in a public voluntary institution. The other institution, the Cancer Institute, is an even brighter testimony to Muthulakshmi’s qualities of head and heart. I experienced this personally in 2005, long after she had passed on. The institute was like no other medical institution I knew – without the feel of either a government or private hospital. As I went through my own treatment, the institute’s underlying approach gradually unfolded: accord priority to saving life at all costs, cutting out the frills, advanced technology for core treatment alone, no differentiation between different classes of patients in medical treatment. Much has been written about the Cancer Institute as a pioneering oncology centre in the country – its outstanding accomplishments in acquiring cutting edge technology, developing stringent protocols and yet giving affordable care; its challenges and limitations. What struck me, above all, is how Dr. V. Shanta, at its helm for many decades, has kept patient care – medical, psychological and social – at the centre. She verily embodies an ethic of care over and above medical protocols. Shanta, however, attributes these features of the Institute to the inspiration and efforts of its founder, Dr. Muthulakshmi, whom she refers to as Mother, and her son Dr. S. Krishnamurthi who was the force behind the institute in Muthulakshmi’s final days and after her passing. Krishnamurthi was a mentor to Shanta, she was his loyal colleague and together they steered the institute to reflect the values and ethos of Muthulakshmi, while striving for excellence. Muthulakshmi herself was inspired to start the institute as a result of a personal bereavement. She lost her sister to undiagnosed cancer in1923. She had nursed her through her last painful days. Amidst her grief, she vowed to establish a specialised hospital for the treatment of cancer. She was inspired by the emerging advances in cancer treatment in the West and in 1925 spent a year at Royal Marsden Hospital, in London, to specialise in the subject. She got the Women’s Indian Association involved in her mission. It was an unusual issue for a women’s organisation to take up but the sheer force and dynamism of her personality made this a major activity of WIA for many years, says Sarojini Varadappan. Muthulakshmi went about her mission with, well, missionary zeal. Her son Krishnamurthi, then a doctor in the Royal Cancer Hospital in London, was not keen to get involved. In an interview with me in 2010, weeks before his death, he remembered with a smile, “I got a telegram, ‘Mother serious. Start immediately’. I came back to find her hale and hearty and what else, I joined her mission.” No one – doctors, funders or the government would take Muthulakshmi seriously. They thought it was a waste of time. There was a complete lack of public awareness about cancer as an illness curable with specialised treatment. Among the various documents of the institute is a printed appeal in 1935 to the King George V Fund Committee from five women’s organisations in the city, mobilised by Muthulakshmi. She was tireless in her crusade and it was through the force of her individual convictions and the mobilisation of her social and political connections that Jawaharlal Nehru laid the foundation stone in 1952 for the first specialised hospital for cancer in South India. The character and thrust of the institute thus become comprehensible only through the personal lives of its three protagonists and their inter- relations. The micro worlds of family and friendship and of ideology and emotion fuelled the dynamism of the macro arena of advanced oncology. And behind the technological and organisational strengths of the institution lies an ethic of care that has evolved through the personal concerns of Dr. Muthulakshmi. While the larger social and historical contexts no doubt impacted upon Dr. Muthulakshmi Reddi’s life trajectory, in many ways, her story exemplifies the idea of ultimately the personal being the political. Kamala Ganesh is a sociologist based in Mumbai. The state today: blame the representatibes The state today is reeling under serious crisis. Bandh , agitations and general strike on various issues have once more become a daily affairs. Students’ now started facing disturbances, proposed midterm exam have to be postponed, private entrepreneurs have to remain shut and the old lady who use to come at Imphal Khwairambandh Keithel to earn a day meal for their children now were once more left with tears on their eyes. Bandh and general strike which had already forgotten by the people for nearly 2 and half years now is hunting the people once again. The previous government led by Congress received maximum criticism due to the frequent bandh and blockade. And after the coming of the BJP government in March , 2017, the Chief Minister N. Biren Singh first agenda was to eradicate the bandh culture and he had shown that for around two years. There were relieves to the parents of the state as they felt safe to the career of their children. The private entrepreneurs felt that they can grow their business and the social thinkers thought that daily wage earner who live on hand to mouth would no longer starve. It was after this government nearly completed 2 and half years that the same regalia that had witnessed by the people of the state during the previous government regime seem to return. After some Ministers and some BJP MLAs started demanding replacement of the Chief Minister, people started witnessing any things like bandh blockade, general strike etc. While saying so it is not that there might be possibility of the rebel MLAs inciting the various sections of people to create chaos in the state. But what Imphal Times felt is that the lack of coordination among the cabinet Ministers, MLAs had already made the government helpless in running the governance. At present the farmers are waiting for water, the manual sand miner labourers are left with no choice but to go with the intense agitation by excavators and truck owners. As those running the government fails to seat together and discussed the issue together to make a collective decision in solving the problem, how on the earth would one expect running a good governance. The present chaos in the society is the result of the political instability in the state. It is over 2 months and keeping it in the way as it is without finding any solution is nothing but an attempt to crumble the government so that the center could impose President Rule in the state. Interlocutor to the government of India RN Ravi had taken oath of office as the governor of Nagaland and when acting as the interlocutor, RN Ravi had made many assurances to settle the Naga issue. Solving the contentious issue of the NSCN-IM – what would have been the best time. Obviously it will be the president rule. Written By: John L. Berggren Craig G. Fraser Menso Folkerts Wilbur R. Knorr Jeremy John Gray The geometric problems in the papyri seek measurements of figures, like rectangles and triangles of given base and height, by means of suitable arithmetic operations. In a more complicated problem, a rectangle is sought whose area is 12 and whose height is 1/2 + 1/4 times its base (Golenishchev papyrus, problem 6). To solve the problem, the ratio is inverted and multiplied by the area, yielding 16; the square root of the result (4) is the base of the rectangle, and 1/2 + 1/4 times 4, or 3, is the height. The entire process is analogous to the process of solving the algebraic equation for the problem (x × 3 / 4 x = 12), though without the use of a letter for the unknown. An interesting procedure is used to find the area of the circle (Rhind papyrus, problem 50): 1/9 of the diameter is discarded, and the result is squared. For example, if the diameter is 9, the area is set equal to 64. The scribe recognized that the area of a circle is proportional to the square of the diameter and assumed for the constant of proportionality (that is, ð/4) the value 64/81. This is a rather good estimate, being about 0.6 percent too large. (It is not as close, however, as the now common estimate of 3 1 / 7 , first proposed by Archimedes, which is only about 0.04 percent too large.) But there is nothing in the papyri indicating that the scribes were aware that this rule geometric was only approximate rather than exact. A remarkable result is the rule for the volume of the truncated pyramid (Golenishchev papyrus, problem 14). The scribe assumes the height to be 6, the base to be a square of side 4, and the top a square of side 2. He multiplies one-third the height times 28, finding the volume to be 56; here 28 is computed from 2 × 2 + 2 × 4 + 4 × 4. Since this is correct, it can be assumed that the scribe also knew the general rule: A = (h/3)(a 2 + ab + b 2 ). How the scribes actually derived the rule is a matter for debate, but it is reasonable to suppose that they were aware of related rules, such as that for the volume of a pyramid: one-third the height times the area of the base. The Egyptians employed the equivalent of similar triangles to measure distances. For instance, the seked of a pyramid is stated as the number of palms in the horizontal corresponding to a rise of one cubit (seven palms). Thus, if the seked is 5 1 / 4 and the base is 140 cubits, the height becomes 93 1 / 3 cubits (Rhind papyrus, problem 57). The Greek sage Thales of Miletus (6th century bce) is said to have measured the height of pyramids by means of their shadows (the report derives from Hieronymus, a disciple of Aristotle in the 4th century bce). In light of the seked computations, however, this report must indicate an aspect of Egyptian surveying that extended back at least 1,000 years before the time of Thales.

Editorial Dr. Muthulakshmi Reddi: A Powerful Face of ... August Page 2.pdf · 2019-08-02  · Chennai; her statue stands in the premises of the Cancer Institute at Adyar, a leading

  • Upload
    others

  • View
    1

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Editorial Dr. Muthulakshmi Reddi: A Powerful Face of ... August Page 2.pdf · 2019-08-02  · Chennai; her statue stands in the premises of the Cancer Institute at Adyar, a leading

Imphal Times Supplementary issue Page No. 2

Letters, Feedback and Suggestions to ‘Imphal Times’can be sent to our e-mail : [email protected].

For advertisement kindy contact: - 0385-2452159 (O).For time being readers can reach the office at Cell Phone

No. 9862860745 for any purpose.

Friday, August 2, 2019Editorial

Courtesy The WireBy : Kamala Ganesh

She has a v isib le presence inChennai; her statue stands in thepremises of the Cancer Instituteat Adyar, a leading centre foroncology in the country. Theroad leading to Besant Nagarfrom Adyar bridge is named afterher. Yesterday, the Tamil Nadugovernment announced that herb irthday would be celebratedevery year as ‘Hospital Day’.For the millennials and post-millennials in the city, however,Dr. Muthulakshmi Reddi is ahazy, hea rsay f igu re o f thena tio nal ist er a – fe isty andarticulate, but as to what exactlyab out, th ey w ould h ave toscratch their heads and think. Onth e o ther han d, the o ld ergeneration of politically awaredenizens of Tamil Nadu knowabout her accomplishments, butmo stly as a chro nologicalnarrative of positions held andorganisations established.Fr om the vantage po in t ofh indsight, I think there is nodoubt that Muthulakshmi was apo werf u l face of na tio nali stfeminism in the first half of the20 th c en tury, w ith al l thecomplexities that this entailed.Her voluminous speeches andwritings are indeed ideologicallydriven, with elements from thediscourses of social reform andna tion ali sm comb ined wi thempathy for the issues espousedby the Justice Party and a benttowards international feminism.But it is in her concrete actions,specifically in estab lishing theAvvai Home in 1932 for destituteand abandoned girls and women,and the Cancer Institu te underthe aegis of the Women’s IndianAssociation (WIA) in 1952 thatwe see the unique nature of hercontribution. The protocols andethos sh e c reated in theseinstitutions are exemplars of anethic of care, insp ired both byfeminism and Gan dhiannationalism. But more on th islater.Bo rn in Pud ukk ottai toChandramma, a former devadasian d Narayanaswami Iye r,pr incipal of the Mahara jacollege, Muthulakshmi had tosurmount huge obstacles createdby her gender and caste, andstruggle to get an education. In 1912, she became the f irstwoman medical graduate from theMadras Presidency; she went onto become an obstetrician.In an interview in 2010, SarojiniVaradappan, a renowned socialworker who worked closely withMuthulakshmi, remembers her asan impressive, even formidable,pe rson ali ty. Imm acu late lydressed in heavy Kanjeevaramsaris pinned with a brooch, andsh in in g d iamo nd ear r ings,Muthulakshmi had a flourishingpractice delivering the babies ofal l th e r ich Mylapo reprofessionals.In f luenced by th e w omen ’smo vement and the na tion almovement, Muthulakshmi turnedher atten tio n to polit ics andpublic life. From 1926 to 1930,sh e w as a member o f thelegislative council in British India,th e f irs t w om an to be sonominated. She became the firstwoman in the world to become theDeputy President of a legislativecouncil.As a leg islator sh e w as anindefatigable campaigner andlobbyist for women’s rights on arange of is sues , includingmedical ins pec tio n in g ir l s’schools, exemption from schoolfees for poor girls, maternity andchild welfare, and reservation forwomen in various structures ofciv ic administration . She wasclosely associated with the All

Dr. Muthulakshmi Reddi: A Powerful Faceof Nationalist Feminism

India Women’s Conference andthe Women’s India Association.Sh e edited the mul tilingu alquarterly journal, Stree Dharma,started in 1918.Mo st n otably, Muthulaksh mibrought in legislation to abolishthe devadasi system and childmarr iage. Th iscampa ign tr igger ed sti f fop pos ition f r om Con gressstalw art s l ike Ra jaj i and S.Satyamurthi. When Satyamurthiargued in the Legislative Councilthat the devadasi system was anan cien t r elig iou s custo m,with devad asi s b eing thecustodians of the traditional arts,she famously retorted that if sucha caste was indeed necessary andsince the devadasis had done itfor so long, why did the Brahminwomen not take over?Muthulakshmi would not haveimagined that decades later shewo uld be cr iti cis ed bycontemporary feminists and hercampaign would be seen as apatronising gesture. SociologistAmrit Srinivasan’s 1985 article,‘Refo rm and Revival : T hedevadasi and her dance’, wasfollowed by much writing on thedevadasis, their original putativerespected social status and theirlater ‘fall’, and the loss for theclassical per for min g ar tstraditions of South India. In particular, Muthulakshmi’scampaign was criticised as it wasperceived as disenfranchisingdevadas is f rom t rad ition alpr iv ileges and d enying themsu bjecth ood and agency.Histo r ian S . An and i, whi lelauding her un den iab lecommitment to women’s rights,sees her as ‘othering’ devadasisan d m ora lising on the ir

liberation from the clutches of thesystem as the only way out. Bu t lo ok a t i t f r omMuthulakshm i’s p ersp ective.Given th e h umil iat ion s s heunderwent, unsurpr isingly shesaw the devadasi system as asocial evil. In fact, one could inferth at to a la rge ex tent , h erpersonal anger was what gaveher campaign its sharp edge.Modern education was, for her,th e answ er – aga inunderstandable given her ownachievements in her professionan d in p ubl ic s erv ice . T hesincerity of her efforts to improvethe situation of devadasi womenis un den iable. Her to neinevitab ly echoed that of theentire social reform movement inthat era, warts and all; it did notec lip se the bas ic dr iv e f oremancipation and equality.In fact, Avv ai Hom e andOr phan age , th at ven erab lein sti tu t ion estab l ish ed byMuthulakshmi in 1931, startedspontaneously when three girlsfrom Namakkal, from devadasifamilies, arrived unannounced ather doorstep one n ight. Theyhad run away from home with

nowhere to go.Immediately she took them intoher own home and that becameAvvai Home, later shifting to itsow n p rem ises. I t h as sin ceexpanded to include a school andalso a teacher’s training school,an d i s on e o f the ear ly andenduring examples of formalisingthe eth ic of ca re in a publicvoluntary institution.The other institution, the CancerInstitu te, is an even br ightertestimony to Muthulakshmi’squalities of head and heart. Iexperienced this personally in2005, long after she had passedon. The institu te was like noother medical institution I knew– without the feel of either agovernment or private hospital. As I wen t thr ough m y o wntr eatmen t, the ins titu te ’sunder lying approach graduallyun fold ed: acco rd p r ior ity tosaving life at all costs, cutting outthe fr ills, advanced technologyfor core treatment alon e, nodifferentiation between differentclasses of patien ts in medicaltreatment.Much has been written about theCancer Institute as a pioneeringoncology centre in the country –its outstanding accomplishmentsin acq uir ing cut tin g ed getechnology, developing stringentpr o to cols and ye t g iv ingaffordable care; its challengesand limitations. What struck me, above all, is howDr. V. Shanta, at its helm for manydecades, has kept patient care – m edical, ps ych olo gica l andsocial – at the centre. She verilyembodies an ethic of care overand above medical pro tocols.Shanta, however, attributes thesefeatures of the Institu te to the

inspiration and effor ts of itsfo und er, Dr . Mu thu lak shm i,whom she refers to as Mother,and her son Dr. S. Krishnamurthiwho was the force behind theinstitute in Muthulakshmi’s finaldays and af ter her pas sin g.Krishnamurthi was a mentor toSh anta , s he w as h is loyalcol league and toge ther theysteered the institute to reflect thevalu es and e thosof Muthulakshmi, while strivingfor excellence.Muthulakshmi herse lf wasinspired to start the institute as aresult of a personal bereavement.She lost her sister to undiagnosedcancer in1923. She had nursed herthrough her last painful days.Amidst her grief, she vowed toestablish a specialised hospitalfor the treatment of cancer. Shewas inspired by the emergingadvances in cancer treatment inthe West and in 1925 spent a yearat Royal Marsden Hospital, inLondo n, to specialise in thesubject. She got the Women’sIndian Association involved in hermission. It was an unusual issuefor a women’s organisation totake up but the sheer force and

dynamism of her personality madethis a major activity of WIA formany years, says Sa ro jin iVaradappan.Muthulakshmi went about hermission with, well, missionary zeal.Her son Krishnamurth i, then adoctor in the Royal CancerHospital in London, was not keento get involved. In an interviewwith me in 2010, weeks before hisdeath, he remembered with a smile,“I got a telegram, ‘Mother serious.Start immediately’. I came back tofind her hale and hearty and whatelse, I joined her mission.” No one – doctors, funders or thegovern ment – would takeMuthulakshmi ser iously. Theythought it was a waste of time.There was a complete lack ofpublic awareness about cancer asan illness curable with specialisedtreatment. Among the var iousdocuments of the institute is aprinted appeal in 1935 to the KingGeorge V Fund Committee fromfive women’s organisations in thecity, mobilised by Muthulakshmi.She was tireless in her crusade

and it was through the force of herindiv idual convictions and themobilisation of her social andpolitical connectio ns thatJawahar lal Nehru la id thefoundation stone in 1952 for thefirst specialised hospital for cancerin South India.The character and thrust of theinstitu te thus b ecomecomprehensible only through thepersona l lives of it s th reeprotagon ists and their in ter-relations. The micro worlds offamily and fr iendship and ofideology and emotion fuelled thedynamism of the macro arena ofadvanced oncology.And behind the technological andorganisational strengths of theinstitution lies an ethic of care thathas evolved through the personalconcerns of Dr. Muthulakshmi.While the larger soc ial andhisto r ical con texts no doubtimpacted upon Dr. MuthulakshmiReddi’s life trajectory, in manyways, her story exemplifies theidea of u ltimately the personalbeing the political.

Kamala Ganesh is a sociologistbased in Mumbai.

The state today: blamethe representatibesThe state today is reeling under serious crisis. Bandh ,

agitations and general strike on various issues have oncemore become a daily affairs. Students’ now started facingdisturbances, proposed midterm exam have to be postponed,private entrepreneurs have to remain shut and the old ladywho use to come at Imphal Khwairambandh Keithel to earn aday meal for their children now were once more left with tearson their eyes. Bandh and general strike which had alreadyforgotten by the people for nearly 2 and half years now ishunting the people once again.

The previous government led by Congress receivedmaximum criticism due to the frequent bandh and blockade.And after the coming of the BJP government in March , 2017,the Chief Minister N. Biren Singh first agenda was to eradicatethe bandh culture and he had shown that for around two years.There were relieves to the parents of the state as they feltsafe to the career of their children. The private entrepreneursfelt that they can grow their business and the social thinkersthought that daily wage earner who live on hand to mouthwould no longer starve.

It was after this government nearly completed 2 and halfyears that the same regalia that had witnessed by the peopleof the state during the previous government regime seem toreturn. After some Ministers and some BJP MLAs starteddemanding replacement of the Chief Minister, people startedwitnessing any things like bandh blockade, general strike etc.While saying so it is not that there might be possibility of therebel MLAs inciting the various sections of people to createchaos in the state. But what Imphal Times felt is that the lackof coordination among the cabinet Ministers, MLAs had alreadymade the government helpless in running the governance.

At present the farmers are waiting for water, the manualsand miner labourers are left with no choice but to go withthe intense agitation by excavators and truck owners.

As those running the government fails to seat togetherand discussed the issue together to make a collective decisionin solving the problem, how on the earth would one expectrunning a good governance.

The present chaos in the society is the result of thepolitical instability in the state. It is over 2 months and keepingit in the way as it is without finding any solution is nothingbut an attempt to crumble the government so that the centercould impose President Rule in the state. Interlocutor to thegovernment of India RN Ravi had taken oath of office as thegovernor of Nagaland and when acting as the interlocutor, RNRavi had made many assurances to settle the Naga issue.

Solving the contentious issue of the NSCN-IM – what wouldhave been the best time. Obviously it will be the presidentrule.

Written By:John L. Berggren Craig G. FraserMenso Folkerts Wilbur R. KnorrJeremy John Gray

The geometric problems in thepapyri seek measurements offigures, like rectangles and trianglesof given base and height, by meansof suitable arithmetic operations. Ina more complicated problem, arectangle is sought whose area is 12and whose height is 1/2 + 1/4 timesits base (Golenishchev papyrus,problem 6). To solve the problem,the ratio is inverted and multipliedby the area, yielding 16; the squareroot of the result (4) is the base ofthe rectangle, and 1/2 + 1/4 times 4,or 3, is the height. The entire processis analogous to the process ofsolving the algebraic equation forthe problem (x × 3/4x = 12), thoughwithout the use of a letter for theunknown. An interesting procedureis used to find the area of the circle(Rhind papyrus, problem 50): 1/9 ofthe diameter is discarded, and theresult is squared. For example, if thediameter is 9, the area is set equal to64. The scribe recognized that thearea of a circle is proportional to thesquare of the diameter and assumedfor the constant of proportionality(that is, ð/4) the value 64/81. This isa rather good estimate, being about0.6 percent too large. (It is not asclose, however, as the now commonestimate of 31/7, first proposed byArchimedes, which is only about0.04 percent too large.) But there isnothing in the papyri indicating thatthe scribes were aware that this rule

geometricwas only approximate rather thanexact.A remarkable result is the rule forthe volume of the truncated pyramid(Golenishchev papyrus, problem14). The scribe assumes the heightto be 6, the base to be a square ofside 4, and the top a square of side2. He multiplies one-third the heighttimes 28, finding the volume to be56; here 28 is computed from 2 × 2 +2 × 4 + 4 × 4. Since this is correct, itcan be assumed that the scribe alsoknew the general rule: A = (h/3)(a2 +ab + b2). How the scribes actuallyderived the rule is a matter fordebate, but it is reasonable tosuppose that they were aware ofrelated rules, such as that for thevolume of a pyramid: one-third theheight times the area of the base.The Egyptians employed theequivalent of similar triangles tomeasure distances. For instance,the seked of a pyramid is stated asthe number of palms in thehorizontal corresponding to a riseof one cubit (seven palms). Thus,if the seked is 51/4 and the base is140 cubits, the height becomes 931/3 cubits (Rhind papyrus, problem57) . The Greek sage Thales ofMiletus (6th century bce) is saidto have measured the height ofpyramids by means of theirshadows (the report derives fromHieronymus, a disciple of Aristotlein the 4th century bce). In light ofthe seked computations, however,this report must indicate an aspectof Egyptian surveying thatextended back at least 1,000 yearsbefore the time of Thales.