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I am in a proof-based Euclidean Geometry class right now at my University, and I brought a certain idea into class, I had been told that I was very close to discovering the same thing Archimedes discovered very long ago. The following may be hard to understand, but simply I can only say that there is only one answer for the value of "Pi", merely because all else would not work:I. Let AB be the diameter of any circle, O its center, AC the tangent at A; and let the angle AOC be one-third of a right angle.Then(1) OA : AC > 265 : 153and(2) OC : AC = 306 : 153.First, draw OD bisecting the angle AOC and meeting AC in D.NowCO : OA = CD : DAso that(CO + OA) : CA = OA : ADTherefore(3) OA : AD > 571 : 153.HenceOD2 : AD2 > 349450 : 23409so that(4) OD : DA > 5911/8 : 153.Secondly, let OE bisect the angle AOD, meeting AD in E.Therefore(5) OA : AE > 11621/8 : 153Thus(6) OE : EA > 11721/8 : 153.Thirdly, let OF bisect the angle AOE and meet AE in F.We thus obtain the result that(7) OA : AF > 2334 1/4 : 153Thus(8) OF : FA > 2339 1/4 : 153.Fourthly, let OG bisect the angle AOF, meeting AF in G.We have thenOA : AG > 4673 1/2 : 153.Now the angle AOC, which is one-third of a right angle, has been bisected four times, and it follows that angle AOG = 1/48 (a right angle).Make the angle AOH on the other side of OA equal to the angle AOG, and let GA produced meet OH in H.Then angle GOH = 1/24 (a right angle).Thus GH is one side of a regular polygon of 96 sides circumscribed to the given circle.And, sinceOA : AG > 4673 1/2 : 153,whileAB = 2 OA, GH = 2 AG,it follows thatAB : (perimeter of a polygon of 96 sides) > 4673 1/2 : 14688ButTherefore the circumference of the circle (being less than the perimeter of the polygon) is a fortiori less than 3 1/7 times the diameter AB.II. Next let AB be the diameter of a circle, and let AC, meeting the circle in C, make the angle CAB equal to one-third of a right angle. Join BC.ThenAC : BC < 1351 : 780.First, let AD bisect the angle BAC and meet BC in d and the circle in D. Join BD.Thenangle BAD = angle dAC = angle dBDand the angles at D, C are both right angles. It follows that the triangles ADB, BDd are similar.ThereforeAD : BD = BD : Dd = AB : Bd= (AB + AC) : (Bd + Cd)= (AB + AC) : BCor (BA + AC) : BC = AD : DB.Therefore(1) AD : DB < 2911 : 780.Thus(2) AB : BD < 3013 3/4 : 780.Secondly, let AE bisect the angle BAD, meeting the circle in E; and let BE be joined. Then we prove, in the same way as before, that(3) AE : EB < 5924 3/4 : 780 = 1823 : 240.Therefore(4) AB : BE < 1838 9/11 : 240.Thirdly, let AF bisect the angle BAE, meeting the circle in F.Thus,(5) AF : FB < 3661 9/11 x 11/40 : 240 x 11/40= 1007 : 66.Therefore,(6) AB : BF < 1009 1/6 : 66.Fourthly, let the angle BAF be bisected by AG meeting the circle in G.ThenAG : GB < 2016 1/6 : 66, by (5) and (6).Therefore(7) AB : BG < 2017 1/4 : 66.Therefore BG is a side of a regular inscribed polygon of 96 sides.It follows from (7) that(perimeter of polygon) : AB > 6336 : 2017 1/4.And.Much more then is the circumference to the diameter< 3 1/7 but > 3 10/71.

Yes ,'Make in India ' is in favour of Indias development.The answer is too long have patience to read this. Here is the progress of ‘Make In India’ Scheme – Sectors, Programs Launched and AchievementsOn 25th September 2014, this dynamic programme gave the corporations a push to invest money in manufacturing products in India, hence “Make in India”.The Make in India campaign is the brainchild of Prime Minister Narendra Modi. It is a movement covering a bouquet of all the sizable sectors of our economy.Just as a reminder, these developments in India are worthy of note:GST has relaxed the procedural system involved in tax and also aided in reducing the production costs.In the recent past, digitization has taken the centre stage. The birth of the company and its survival has been made easier by a seamless online system.The new Insolvency and Bankruptcy Code has your back during your rainy days by a robust restructuring mechanism.Schemes like Jan Dhan Yojana and Prime Minister’s Jan Dhan Yojana aim at financial inclusion of all the citizens.The term Foreign Direct Investment has been doing the rounds for a while now. Liberalization of Foreign direct investment has been brought about an increase in the inflow of funds and has also helped in making India an open economy. The after effects are sure to be positive due to job creations.Connectivity is key to expand the businesses. The Sagarmala programme and Bharatmala Pariyojana Programme are trying to achieve the same.Technology did not have its presence in the rural areas. However, now, with BharatNet making digital delivery of various services across the country is initiated.India is Worlds No 4 in terms of its capacity to harness power from winds and Worlds No 6 in solar power.Further, ease of doing business is the cardinal aspect under the Make in India scheme which will motivate the companies to invest.The status of individual sectors under Make in India schemeAutomobile and Automobile ComponentsIndia is the largest manufacturer of two-wheelers,three-wheelers, and tractors in the world. India has a competitive cost advantage over its counterparts. We also have a pool of masterminds who are serving worldwide as a strong workforce1. Faster Adoption and Manufacturing of Hybrid and Electric vehicles (FAME) and National Electric Mobility Mission Plan 2020 (NEMMP) has been launched to promote electric cars.2. National Automotive Testing and R&D Infrastructure Project (NATRIP) centres are set up3. 100% FDI under automatic route subject to all applicable regulations and law is availableThe top players have inaugurated manufacturing units namely:1. ISUZU motors in Sri City Andhra Pradesh2. Tata Motors & Fiat jointly have opened up in Ranjangaon, Pune3. Suzuki Motors in Ahmedabad4. Mercedes Benz In ChakanRise in AutomobilePercentageProduction2.60%Domestic sales:Passenger vehicles7.24%Commercial Vehicle11.51%Three-wheeler1.03%Two-wheeler3.01%Exports1.91%Rise in Automobile ComponentsPercentageTurnover8.80%Exports22%AviationThe aviation sector is expected to take a boom when we land in 2020. India currently occupies 9th position in the world and is soon expected to reach the skies1. Ude Desh ka Aam Nagrik (UDAN) was introduced for regional connectivity2. Incentives in the form of tax concessions are provided3. National civil aviation policy 2016 was announced for establishing an integrated ecosystem, to encourage tourism and increase employment4. Airports are being developed under the public-private partnership mode to encourage private participation5. GPS Aided Geo Augmented Navigation system (GAGAN) to support direct air routes, reduce fuel consumption and improve safety is initiated1. The passengers carried by scheduled domesticairlines have increased by 29%2. Common User Domestic Cargo Terminals have been operationalized in 13 cities so as to facilitate everything related to cargo services under one roof.BioTechnologyThe biotechnology industry is an industry where India has grown in leaps and bounds. The industry owes its success to the R&D activities and growing government initiatives1. FDI Policy100% FDI dor Greenfield Pharma via the automatic route 100% FDI for Brownfield Pharma. Here, in case of FDI up to 74% automatic route is available and beyond 74% government route has to be taken 100% FDI for medical devices via the automatic route 2. Biotechnology Industry Research Assistance Council (BIRAC) was set up to assist the industry through funding, mentoring, handholding and infrastructure support1. Current Good Manufacturing Practices(CGMP) a plant was inaugurated in 2016 for the manufacture ofPhytopharmaceuticals2. A virtual centre was launched across fiveIndian Institutes of Technology, in 2015, to develop and advancetechnologies in the area of biofuels3. 30 Bio-incubators and Biotech Parks weresupported/established from April 2014 to September 20164. First indigenously developed and manufactured rotavirus vaccine ‘Rotavac’ was launched in 2015Chemicals and PetrochemicalsThe Chemicals industry serves as a backbone to many other industries which makes it a lucrative option. Factors like raw material availability and innovation provide an incentive to the companies to get rolling1. The Assam Gas Cracker project is one of the biggest projects which is expected to produce about 2.8 lakh MT polymers per annum and also expected to provide employment to 100000 people indirectly2. A scheme is developed to set up need-based plastic parks with good infrastructure facilities with financial assistance up to 50% of the project cost1. The FDI equity inflows in the sector increased by 107%2. 0.44 Million MT Per Annum Polypropylene Plant is commissioned at MangaloreConstructionThe demand for real estate and infrastructure projects has been on an uphill over the years. The identification of smart cities has been a smart move which intends to utilize the resources in the best possible manner1. A city challenge competition was held under the 100 smart cities missions with an intention to achieve infrastructure development2. Atal Mission for Rejuvenation and Urban Transformation (AMRUT) is a mission which concentrates on providing basic infrastructure facilities3. Swachh Bharat mission established to promote healthy sanitation practices4. Heritage City Development and Augmentation Yojana (HRIDAY) focuses on revitalizing the Indian Heritage sites5. The Real Estate (Regulation & Development) Act, 2016 has been the shining star of this sector1. 1.7 million houses have been constructed under Pradhan Mantri Awas Yojana (Gramin) houses2. The construction sector is the industry which stands 2nd in line in terms of providing employment, after agriculture. A whopping 35 million people have been employedDefenceIndia has opened its doors of the defence sector to privatisation which was a very essential step to leverage the domestic markets and meet the defence needs1. The opening up of the defence sector to the private sector is paving the way for strategic partnerships2. 100% FDIi. Upto 49% automatic routeii. Above 49% government route3. A ‘Make in India’ portal for Defence Productionhas been launchedWhich provides policy and procedural issues which are of importance forthe defence manufacturing industry1. Various products manufactured in India like HAL Tejas Light combat aircraft by sourcing 95% of the resources required locally2. Defence equipment amounting to INR 2059.18 Crore have been exported to 28 countries in FY 2015-16Electrical MachineryIn the electrical machinery sector, Indian manufacturers are at their peak of competitiveness with regards to product design, manufacturing & testing facilities. A big chunk of investments are made in research and development which will help India accelerate its manufacture1. Incentives for capacity addition in power generation will serve as a means to increase the demand for electrical machinery2. 100% FDI is allowed in the automatic route subject to rules and regulations1. This industry recorded a double-digit growth rate of 12.8% over 2017-182. India has turned around from a net importer of electricity to a net exporter of electricityElectronic SystemsElectronic system is an area where the focus has been on import substitution. India being a labour rich country has a forte which needs to be taken advantage of.1. The Modified SIPS scheme has been developed in order to attract investment into this sector2. Export incentives 2-3% are made available under the Merchandise export from India scheme3. The export promotion capital goods scheme offers zero customs duty for import of capital goods used for pre-production, production and post production1. Around 38 mobile manufacturing units have been set up which have created employment of about 383002. Under Digital Saksharta Abhiyan(DISHA)around 99.56 lakh candidates have been enrolled for training3. In 2017 this industry witnesses a remarkable jump of 27% where in the total volume reached 1.57 Lakh Crore from 1.43 Lakh Crore in 2016Food ProcessingIndia is in a position to provide hygienic food processed and packed by utilisation of modern technology. Nivesh Bandhu is a platform which provides a one stop solution to investors in the area of food processing, aiding them in decision making and providing incentives1. Reserve Bank of India has classified loan to food & agro-based processing units and Cold Chain under agriculture activities for Priority Sector Lending (PSL) subject to the aggregate sanctioned limit of USD 15.38 million per borrower which will ensure a good flow of credit to the entrepreneurs2. A special fund called Food Processing Fund amounting to USD 300 millions has been deposited with the NABARD in order to provide funds to designated food parks and individual food processing units in the designated food parks3. Reduction of excise duty and customs duty has been a fiscal incentive which helps boost up the industry1. The growth rate of Gross Value Added has increased from 1.91% in 2013-14 to 5.78% in 2014-15 at constant prices2. There has been a FDI equity inflow of USD 1.7 Billion from April 2014 to December 20163. 88 cold chain projects have been operationalised out of the 134 projects which had been sanctioned4. The government had sanctioned 42 mega food parks of which 8 have been operationalised. Every mega food park is set to create employment opportunities for about 5000-6000 people and benefit 25000-30000 farmersIT and BPMIT + IT= ITIndian Talent + Information technology = India Tomorrow.The Information technology sector contributes a countable share to the exports. This industry is the largest private sector employer providing millions of job opportunities1. Favourable government policies and initiatives serve as an incentive to invest in this sector2. The Digital India campaign has pumped in a lot of investment with digital delivery standing as a focus point1. Total FDI equity inflow in Computer software and hardware sector saw a major growth from 2.3 Billion to 5.9 BillionLeatherThe leather industry is striving to succeed with 55% of its workforce below 35 years of age.The demand for leather products is on the rise and the concept of utilising young labour with oozing energy is helping this sector flourish1. The leather product sector is entirely de-licensed which serves as an icing on the cake2. Grants are provided in the following manneri. 30%-on cost of plant & machinery to Micro and Small Unitsii. 20%-To other unitsiii. 50%-for establishment of Mega Leather Clustersiv. 50% for upgradation/installation of Common Effluent Treatment plants1. The FDI equity inflow amounted to USD 53.39 Million in this sector2. India boasts of being the 2nd largest producer of footwear and also the 2nd largest exporter of leather garments3. Under the Indian leather development programme, primary skill development training has been imparted to 117499 and 80% of these have been placed as on January 2017Media & EntertainmentDespite all the criticism against television, India has the 2nd largest TV Market in the world. Growth in the number of multiplexes, increased liberalisation and tariff relaxation serve as incentives to start exploring into this industry1. In order to give a lift to the exports, treaties have been signed with countries like Italy, Brazil, the UK and Germany2. Basic Custom duty for digital still image video camera has been brought down to Zero3. National Film Heritage Mission has been introduced to archive films through the National Film Archive of India1. Growth in FDI in the information and broadcasting area from USD 1.9 Billion (2010-14) to USD 3.4 (2014-18)Billion which is a good 1.8 times within a span of 8 years2. 283 billion to 263 Billion, a 20 billion leap is the growth recorded by the print industry3. The 24*7 DD Kisan channel saw a huge response with a total viewership of 1.52 Crores within a very short span of 7 monthsMiningMining is the crux of the Indian economy. Many industries depend on it to procure their raw materials.1. The Mines and Minerals Development and Regulation Act 1957 (MMDR) had been amended with greater transparency as its motive2. District Mineral Foundation set up for grievance redressal and also to improve the image of mining1. In terms of Gross Value Added this sector has grown by 10.5% in 2016-17 and 12.5% in 2017-182. While the world market is shaky due to the chinese economy issues, India has experienced a surge in the production of minerals3. By November 2016 17 mineral blocks across 7 states have been auctioned which has resulted in additional revenues amounting to INR 47551 Crores and total revenues of INR 59639 CroresOil and GasThe mushrooming population and the flourishing economy of India has helped the Oil and Gas Industry in a mighty big way. Many opportunities exist for the development of underground coal, its gasification and conversion to liquids1. Hydrocarbon Exploration & Licensing Policy (HELP) provides for a uniform licensing system, no awaiting a formal bid round and incentives on royalty rates for offshore blocks2. An additional depreciation of 15% on installation of capital equipment acquired is permitted1. In Gujarat India has invested in refineries specially for exports which has made India a net exporter of petroleum while we are a net importer of crude oil2. Refining capacity of India has been expanded by 15 Million Metric Tonnes Per Annum due to the commissioning of Paradip Refinery In February 20163. Crude Oil Strategic storage of 5.33 MMT capacity was built at Visakhapatnam, Mangalore and PadurPharmaceuticalsMedical Tourism is moving uphill due to the expertise India possesses in this space. India’s cost of production is considerably lower than USA and half of the cost in Europe1. In order to make healthcare more reachable new Health and Wellness centres have been established2. The National Pharmaceutical Pricing Policy 2012 mainly focuses on the regulation of the price of drugs1. The pharmaceutical industry has seen an upturn from INR 158671 Crore in 2013-14 to INR 177734 Crore in 2014-15 to INR 204627 Crore in 2015-162. Indian Drugs and Pharmaceuticals Limited has enabled the mass manufacture of products in the field of Oncology, Nephrology and Cardiology3. Pharma Jan Samadhan, a customer grievance redressal system launched in March 20154. Pharma Sahi Dham provides real-time information on prices of medicinesPorts and shippingIndia has 12 major ports and 64 minor ports handling the Import Export in order to attract investment, the Government has allowed 100% FDI in the shipping sector1. New Berthing Policy for Dry Bulk Cargo for all major ports was introduced to facilitate movement of higher cargo throughput from major ports2. Funds amounting to USD 25 Million for major ports and USD 21 million for minor ports have been earmarked1. A giant leap was seen in FDI from USD 0.5 Million (2010-14) to USD 2.5 Billion (2014-18)2. Turnaround time at ports reduced by 25% (2012-13 vs 2015-16)3. Under the Sagarmala project, a total of 173 projects with an investment of INR 4 Lakh Crore introduced during 2016-17RailwaysIndia stands tall with a ranking of World No 3 in terms of the railway network spanning more than 66030 Kms. 100% FDI provides an opportunity for high speed railways and electrification.Automatic Ticket Vending Machines and computerized passenger reservation systems aim at passenger convenience1. Public Private Partnership mode to enhance passenger amenities2. Project Swarn targets on improving passenger experience and in order to facilitate this 14 Rajdhanis and 15 Shatabdi trains are identified3. Mission Raftaar has at its core the the doubling of average speed of freight trains and also increasing the speed of all non suburban trains1. A noteworthy achievement in the year 2017-18 is 51 trains have been speeded up by more than a hour2. The Gatimaan Express is the fastest train in India which covers a distance of 188 Kms in 1 hour and 40 mins3. In order to set up an electric locomotive factory at Madhepura India has joined hands with M/s Alstom Manufacturing India and for setting up a diesel locomotive factory with GE Global Sourcing India Pvt Ltd at Marhowra amounting to a total of INR 40000 CroresRenewable EnergyThere has been an ever increasing demand for energy in the country and it is imperative to use renewable sources of energy. Reducing India’s dependence on expensive imported fossil fuels is the goal in this sector1. A bouquet of fiscal incentives have been provided which include:i. Enhanced Depreciationii. Concessional Custom dutyiii. Excise duty exemptioniv. Income tax holidays for 10 years2. In order to encourage usage of renewable energy sources clean environment cess has been doubled form INR 200 per tonne to INR 400 per tonne.3. To promote clean energy co-operation a joint Indo-US PACE Setter fund has been established with a contribution of USD 4 Million1. The world’s largest solar power plant was commissioned in Tamil Nadu with a huge capacity of 648 MW2. 140% increase in the solar power capacity (2014-16 vs 2012-14)3. 34 Solar parks have been sanctioned to 21 states and INR 356.63 Crores has been provided to Solar Energy Corporation of India for the sameRoads and HighwaysThe government is taking a major step in upgrading highways and expressways. Government is encouraging the development of this sector by providing subsidies, tax exemptions and duty free imports of high capacity and modern, road construction equipment1. The government takes burden of cost on project feasibility study,shifting of utilities,environment clearance etc2. Subsidy of upto 40% of the project cost is provided as an incentive3. The Ministry of Road Transport and Highways(MoRTH) has provided funds to the state government to develop state roads1. Achievement for the year 2017-18 are 8088 km of road length awarded,7589 km of construction completed and 2156 km of highways tolled2. The length of the national highways has seen substantial growth from 91287 km in 2014 to 115435 km in 20173. After the introduction of Electronic Toll Collection System the fee collected has increased from USD 27 million in Jan 2017 to USD 43 Million in Nov 2017SpaceIndia has skyrocketed its way into the space sector literally and even metaphorically. Our country’s cost effective programme has made it a launchpad for many countries and is hopeful of calling itself as the world’s launchpad1. GSLV III launched for satellites which are heavier in nature weighing about 4500 to 500 kg2. ISRO has entered into co-operative arrangements with 33 countries and 3 multinational bodies1. Antrix Corporation Limited has undertaken various initiatives for marketing of space products and services at a global level2. India is the first nation in the world to reach Mars successfully in the 1st attempt. The spacecraft was called MangalyaanTextiles and GarmentsTextiles and Garments sector has made India a one-stop solution for textile and garment needs. Being one of the largest producers in the world and second largest exporter of cotton in the world, this scheme has made India world famous. Women empowerment is seen in the right sense here as 70% of its workforce consists of women1. The Merchandise Exports from India Scheme served as an incentive by providing duty rewards to the extent of 2-5% of FOB value2. To reduce the burden on Indian investors,interest equalisation scheme was introduced3. Special Textile Packages have been approved with a view to create jobs,encourage exports and also to draw in investments1. The total exports took a leap from 13% to 15% (2013-14 vs 2015-16)2. There has been a substantial growth in FDI of 2.5 times (2010-14 vs 2014-18)3. The existing textile park has seen the entry of new production units totalling to 200 in number in the recent past creating jobs for 11000 personsThermal PowerThe thermal power industry has various incentives which ensure adequate return on investment to companies. Expansion in industrial activity and growing population are factors which will encourage companies1. The revised tariff policy 2016 guarantees a good return on investment and ensures safety of the investments to the investors2. The Ultra Mega Power Projects having a huge capacity of 4000 MW have been set up by the government of India in order to bear the fruits of economies of scale and fast capacity addition1. India boasts of having the fifth largest installed capacity in the world2. The electricity generation increased by 5.9%(2016-17 vs 2015-16)3. April 2014 to October 2016 has witnessed an addition of 50471.41MW to the generation capacity.4)98.8% of the villages have been electrifiedTourism and hospitalityThe tourism and hospitality is the lifeblood of an economy.Tourism is the third largest foreign exchange earner next in line after gems and readymade garments in India. Private-public partnerships will be the focus for India to see this Industry makes its mark in the future1. Swadesh Darshan scheme had been launched to serve mass and niche tourism2. The National Mission for Pilgrimage Rejuvenation and Spiritual Augmentation Drive had the beautification of pilgrimage sites as its focus3. The e-tourist visa facility has been extended to travellers of 150 countries1. India crawled up 13 places from 65 to 52 as per the Travel and Tourism Competitiveness Index 2015 of the World Economic Forum2. Foreign Exchange Earnings have increased from INR 1351 Billion(FY 2015-16) to INR 1556 Billion3. This sector is among the top 10 sectors when it comes to the FDI inflow.The FDI inflow has increased by 72% (2015-16 vs 2014-15)WellnessThe demand for AYUSH (Ayurveda, Yoga, Naturopathy, Unani, Siddha) has seen an upsurge over the years. The adverse effects of other drugs and its high cost has caused this turnaround and this is here to stay1. 100% FDI is permitted in the AYUSH sector2. Central Sector Scheme for promotion of International Cooperation has as its aim the creation of awareness about the strength and utility of AYUSH and its promotion at the international platform3. The government of India has set up the AYUSH Sector Innovation Council1. India stands as the second largest exporter of AYUSH and herbal products2. This industry has a huge potential to create jobs to the level of 3 million.Over and over again the world is invited to come to India and have faith in the country because India promises a fair system and the best it can, without leaving any stone unturned.If size really mattered the elephant would have been the king of the jungle. Let’s Roar and make our presence felt!Thank you … Have a great day.