सिद्धांत सिरोमणी - गौरव व. मानकर (B3)
Bhaskara (1114 – 1185) (also known as Bhaskara II and Bhaskarachārya
गणित आठवले की आठवते भारतीय गणितज्ञ व
तयाांचा इततहास, जगाला तयाांनी दिलेली सुत्र.े या माललकेत आपला ठसा जगावर उमटविारे ज्येष्ठ व श्रेष्ठ गणितज्ञ 'भास्कराचायय’ याांच्या नावाचा उल्लेख केल्यालिवाय पढ ु े जाता येिार नाही.
भास्कराचायाांचा 'सिद्धांत सिरोमणी' हा गणितावरील प्रमुख ग्रांथ आहे . या ग्रांथाचे लललावती, बीजगणित, ग्रहगतनताध्याय, गोलाध्याय हे चार खांड आहे त.
1. सििधवती : लललावातीमध्ये बीजगणित व महततवमापन यावर २७८ श्लोक आहे त. यामध्ये सांखयाांच्या स्थान, सांखयाांची बेरीज, वजाबाकी इतयािी तसेच व्याज गणितीय व भूलमतीय श्रेढी, प्रतलीय व घनभलू मती व काही पररिामाांचे कोष्टके दिली आहे त.
भास्कराचायाांनी आपल्या लललावती या ग्रांथात प्रारां भीच सांखयाांच्या गाननासाठी एक सुांिर सुभाषित दिले
जाते. एक ििित सहस्य: आयत ु लक्ष प्रयत ु कोष््य क्रमिः अबुियम अब्जम खवय तनखवय महापद्य िांकाव: तस्मात
जालाधिश्र्व अतयन मध्य परािमय इतत ििगुनोततर सांज्ञा.
सांखयाया स्थानां व्यवहायय कृतः पूववः उजवीकडून डावीकडे
अनुक्रमाने एकम, ििम, ितम, सहस्त्र, अतयुत (ििसहस्त्र) , लक्ष, प्रतयत ु (ििलक्ष), कोटी, अबि ुय (ििकोटी), अब्ज, खवय, तनखवय, महापद्य, िांकू, जलिी, अतयान, मध्य, परािय दह सांखया स्थाने आहे त.
या सांखया सांज्ञा िहाच्या घाताांकाच्या स्वरुपात पढ ु ील प्रमािे ललदहता येतात.
एकम
1
100
ििम
10
101
ितम
100
102
सहस्त्र
1000
103
अतयत ु (ििसहस्त्र)
10000
104
लक्ष
100000
105
िि लक्ष (प्रतयत ु )
1000000
106
कोटी
10000000
107
अबि ुय (ििकोटी)
100000000
108
अब्ज
1000000000
109
खवय
10000000000
1010
तनखवय
100000000000
1011
महापद्य
1000000000000
1012
िांकू
10000000000000
1013
जलिी
100000000000000
1014
अन्स
1000000000000000
1015
मध्य
10000000000000000
1016
परािय
100000000000000000 1017
2. बीजगणित : बीजगणित या िस ु ऱ्या खांडात २१३ श्लोक
आहे त. यामध्ये अज्ञात सांखया िियवण्यासाठी वापर केला
जातो. तसेच िन, ऋि, िन् ू य, अन्याक्त करातनसांखया,
एकवािी, अनेकाविी,द्षविात समीकरिे, अन्याक्ताांच्या गुिाकाराच्या क्रक्रया याषवियी मादहती दिलेली आहे . 3. ग्रधहगनितधध्यधय : या ततसऱ्या खांडात ४३४६ श्लोक आहे त. यात ग्रह सांबि ां ीचे व पांचाांगाचे गणित दिलेले आहे . 4. गोिधध्यधय : या चवथ्या खांडात २१०० श्लोक असून गोलचा अभ्यास, स्वरूप भूगोल व खगोल, िियक गोलाची कृती,
गोलीय, त्रीकोनलमतीची ततवे, ग्रहिाांचे गणित असे १३ षवभाग आहे त. गणितासारखया अमत ृ आणि गहन मनोरां जनातमक व
काव्यातमक पद्धतीने लिकषविारे ते आद्य पांडडत होते. अिा या गणित षवियाच्या बाबी मध्ये ज्ञानाला तोड नाही.
PIC Microcontroller -Mahesh D. Pithe (3U1) What is a pic microcontroller? The PIC Microcontroller is a low cost 'computers on a chip' manufactured by Microchip; they allow electronic designers and hobbyists impart intelligence and logic to a single chip for special purpose applications and products. The PIC microcontroller programming is done using the popular software ‘Mikro C’. This powerful yet easy to program into a 40-pin package is upwards compatible with the PIC16C5X, PIC12CXXX and PIC16C7X devices. We are going to explore the world of microcontroller, microcontroller programming and embedded systems with PIC16F877A. It is has five portsport A, port B, port C, port D and port E. How to program microcontroller? Which is the program for microcontroller? These are the commonly asked questions by microcontroller beginners. An embedded system design is easy with the help of embedded C programming. Let’s start studying about microcontroller and embedded C
programming for microcontroller PIC using Mikro C Pro. This article deals with the basic connection diagram and a LED blinking program of PIC microcontroller. Why PIC is used/ Why PIC is Popular?
High Speed High Performance RISC (Reduced Instruction Set Computer) CPU Instruction Set Simplicity Integration of Operation Features Programmable Timer Options Interrupt Control EPROM/OTP/ROM Options Inbuilt Modules Low Power Consumption Wide Operation Voltage Range: 2.5 to 6 Volt Programmable Code Protection Mode Power Saving Sleep Mode
PIC16F877A Features
High performance CPU Only 35 instructions
All are single cycle instruction excluding for program branches. Operating speed is DC to 20MHz. 8Kx14 word of flash memory 368x8 bytes of data memory 256x8 bytes of EEPROM data memory Interrupt compatibility Power on reset Power up timer and oscillator start up timer Watch dog timer with its own chip RC oscillator for reliable operation Programmable code protection power saving SLEEP mode Low power, high speed CMOS FLASH/EEPROM technology In circuit serial programming capability via two pins Processor read write access to program memory Single 5v in circuit serial programming capability In circuit debugging via two pins Wide operating voltage range High sink or source current Low power consumption
Basic connection diagram of PIC Microcontroller To start a Microcontroller project you need to configure the PIC as follows (Basic Requirements)
(LED is connected at the 7th pin of Port B is just for an example)
Components required 1. Power supply 2. PIC16F877A Microcontroller 3. Resistors ¼ watt (1kΩ x 2) 4. Capacitors (22pF x 2)
5. Electrolytic capacitor (1ÂľF) 6. Push button switch (for resetting the PIC) 7. Crystal (4MHz) 8. LED
Example Program [LED Blinking] The program codes are well commented for better understanding. void main() { TRISB=0X00; //Initializing PORT B as output port w hile(1) //Infinite loop { PORTB=0XFF; //Setting all bits of PORT B as HIGH delay_ms(100); //Calling inbuilt delay program PORTB=0X00; // Setting all bits of PORT B as LOW delay_ms(100); //Calling inbuilt delay program } }
Reverse Engineering -Shreyas V. Lokhande (3M) Reverse engineering is the process of discovering the technological principles of a device, object, or system through analysis of its structure, function and operation. It often involves taking something apart and analyzing its workings in detail to be used in maintenance or to try to make a new device or program that does the same thing without using or simply duplicating the original Reverse engineering as the name suggests is the process of tracing down the underlying technology of any industrial product to manufacture high quality products. It is basically a technique that replicates an existing component, product or sub-assembly without the effort of documentation, drawings or computer model. Reverse engineering is gaining much popularity by the day . Reverse engineering technique saves time, resources and leads to the manufacture of an excellent product. This calls for utilization of high end techniques such as Reverse Engineering
Forward engineering is done by the method of water fall model. The blok diagram of waterfall model is as shown in fig.
As we know RE is Reverse forward engineering, henceforth Reverse Engineering moves through this process in reverse .In Reverse engineering, it may not end up with the same implementation but certain modification can be done.
Need for Reverse Engineering
There is inadequate documentation of the original design The original manufacturer no longer exists, but a customer needs the product The original design documentation has been lost or never existed Some bad features of a product need to be designed out. For example, excessive wear might indicate where a product should be improved To strengthen the good features of a product based on long-term usage of the product To analyze the good and bad features of competitors’ product To explore new avenues to improve product performance and features To gain competitive benchmarking methods to understand competitor’s products and develop better products The original CAD model is not sufficient to support modifications or current manufacturing methods The original supplier is unable or unwilling to provide additional parts The original equipment manufacturers are either unwilling or unable to supply replacement parts, or demand inflated costs for sole-source parts To update obsolete materials or antiquated manufacturing processes with more current, lessexpensive technologies
Process of Reverse Engineering Reverse Engineering entails a variety of activities including analyzing components and their inter-relations, creation of prototypes in some or the other level of abstraction and production of physical representation of the product. Replication of existing products or sub-assemblies by capturing the physical properties such as material properties and features is done under Reverse Engineering. It involves:
Identify the system’s components and their interrelationships Create representations of the system in another form or a higher level of abstraction Create the physical representation of that system
Reverse Engineering Software: Rapid form XO Redesign: This software makes the process of creating parametric CAD models from real world parts faster and easier by utilizing a design process and user interface that are instantly familiar to CAD users. Geomagic Studio: Geomagic Studio transforms 3D scan data and polygon meshes into accurate 3D digital models for reverse engineering, product design, rapid prototyping and analysis.
RevWorks: RevWorks® enhances the state of the art for CAD-Driven Reverse Engineering™. In linking SolidWorks to your 3D digitizer or coordinate measuring machine (CMM), RevWorks opens the door to greatly enhanced productivity. DezignWorks: The standard in reverse engineering for SolidWorks, allowing users to create complex 2D and 3D shapes, with a Romer, Faro, Baces, or MicroScribe Digitizer/Portable CMM. Rhinoceros NURBS Modeling for Windows: Rhino can create, edit, analyze, and translate NURBS curves, surfaces, and solids in Windows and offers full support for all 3D Digitizers and Portable CMMs. Reverse Engineering applications are commonly found in:
Rapid prototyping General manufacturing and inspection Plastics manufacturing Composite manufacturing Steel manufacturing Automotive manufacturing Aerospace manufacturing Heavy equipment manufacturing Shipbuilding