Division of segments into as many equal parts

,OY: J\UDI]ITIB ER &IVINDRA PATIL. COLLEGE: INDIAN INSTITUTE OF TECHNOLOGY, BANARAS HINDU UNIVERSITY STREAM: ELECTRICAL ENGINEERING.

YEAR: 3rd year.

TOPIC OF MANUSCRIPT: DIVISION OF SEGMENTS INTO AS MANY

EQUAL

PARTS

I

HAVE GENERATED A METHOD TO ANY SEGMENT OF ANY GIVEN MAGNITUDE INTO AS MANY EQUAL PARTS IVHICH IS EXTREMELY HANDY AND JUST NEEDS A SETSQUARE AND A PENCIL BUT IF WE HAVE AGRAPH PAP. ER WE NEED ONLY A PENCIL AND A SCALE. lVE WONT NEED A SET QUARE FOR WE NEED TO DRAW ONLY PERPENDICULAR LINES WHICH WE HAVE READY MADE ON A GRAPH PAPER. THE METHOD GOES AS FOLLWS: LETS HAVE A LENGHT OF ANY GIVEN DIMENSION I MEAN LENGHT AS GIVEN. 7.5CM FOR INSTANC: ..1f,8Tf;-i:CALL THIS SEGMENT AS AB.

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LETS FOR EXAMPLE AIM IT TO DIVIDE THIS SEGMENT INTO 9 EQUAL PARTS. AND LETS TAKE A PLAIN SHEET THAT IS WE DONT HAVE A GRAPH PAPER. SO WE NEED TO USE A SETSQUARE A VERY IMPORTANT INSTRUMENT. NOW DRAW A LINE ON THE PAPER AS SHOI]N. DRAW ANOTHER LINE PERPENDICULAR TO IT. LETS CALL THE INTERSECTION POINT AS THE FOCAL POINT AND DENOTE IT BY O. NOhT

AS SHOWN BELOW AND TAKE ITASA SEGMENT MADE UP OF 9 EQUAL PARTS OF ANY DESIRED LENGHT ( 9 BECAUSE iVE WANT TO DIVIDE THE SEGMENT AB INTO 9 EQUAL PARTR FOR CONVINIENCE I TAKE THIS SEGMENT AS 9CM. LETS CALL THIS SEGMENT LM. LETS I'{ARK THIS EOUAL PARTS OF 1cm ON SEG LM. NOW DRAW ANOTHER SEGMENT

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THE POTNT O IVITH ALL THIS MARKED POINTS

THE SETSQUARE AFTER ACCURATELY MEASURING THE SEG AB WE ADJUST THIS MEASURED QUANTITY WHICH TS 7.5CM( WE CAN ALSO USE A BOTH LEGS POINTED DIVIDER FOR MEASURING PURPOSE) IN THE TRIANGLE OLM SO THAT IT IS PERPENDICULAR TO THE LINE OM AND DRAW IT AS SHOWN. NOW USINq

LINES STARTING

NOW

14ENT

oTo

FROM SEG AB

LM ARE DIVIDING THE

THE MARKED POINTS OF THE SEG-

INTO 9 EOUAL PARTS.

PROOF:;LETS LABEL THE ENTIRE FIGURE AS SHOWN. h7E WILL OBTAIN OUR PROOF BY THE THEORY OF SIT4ILAR TRIANGLES.

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