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A study in maths

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  • >T]+| eTT. CjTqy&Tq dqTq e \eTTH >\ >TsT|s+|s>eTT> dTsT|C|T\ |e, sXdeTT\T |e
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  • >BjT&q eeTTe+{ dT]dT+~.>DXd+ b]uw+> eTTqT BseeTT (Ellipse) n eeV]dT+~.(#. 1e eTT.)

    k>BjT&q e dT]dT+~.(# 2e eTT)

    |& s+&T sUeTT\qT deVs+#d@s+> u$+qsTT |sdseTT K+&+#T=qT s+&TBseeTT\T > |wY |e#H nqsTTd u$d,eTq+eTT+ (|j)` 1.\ (Head), 2.&s (RightWing), 3.m&eTs (Left Wing), 4.XseTT (Body/ Trunk), 5.|#eTT(Tail) uddT+~.(+ 3). B |wT nqeTjTX+> eeV]+|&T#Tq d\Xs d++> #| deTqsTTdT+~. ~X> d,| u>

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  • > >DXdDXdeTT dNos X+(Cone) eT]jTT H$
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  • > s+#&+~. B eT\+ d+d

    20 |PsMTe+k TD XyTq ysT> #|qeds+ TD\ deVs ds|+> u~dTq~. eT&T>TD\T | (Universe) jTT deT\eTT (Equilibrium) qTd+sd +{sTT. eq deTuVQ uTeTT >TDeTT\# |]s+# &T#TqdeT d >\ | |s|eT eTq+ d+u$+#*.5. #sTsdeTT (Square) : ~L#eTT\T> H\T>T ~>q_+T dssK\# \+esZeTT \T|> Hs&q #TsdeTTqT u|seTTn+{sT. u|seTq> ~vD\ |]y|yTq deT#TsdeT b]uw+>s+# e#TqT. >DXd+ #Tsk eTDXd |]uwqqTd]+ eTT+T]+ d\+> $e]+#TH+. eeTTsUeTT\{ eT\sDyTq~. eqH B ysDyTqVeT |PseT |s=HsT. |Ps VeTT\qT d+]+#TqB eTs$ ueTT\| eqe+|]y|yTq u\eTT| >\ dsdeT\ esT s eTT>qT ~vD\yT #|&+ @eT+ $&s+> $+> qd |]>q\+(X+) L& eyTq ks+X+. eq n~ VeTT jTT |]qT |PseTH |sTqT ]+#&q~. > eeTT jTT VeTTnH sX+ bse]+> |d, |PseTH e| XdjTyTqeT\+> s+#&qV+#*. eeTT jTT s+&T $

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  • >, |T, v3. #esZ ` #, #, , sa, x4. esZ ` , s, &, &, D5. esZ ` , D+#&q~. s+&TdeejTeTT\ eZsD, drsDeTT\qT, eseTeTTqT n+seTT qTq|{, s+&T deejTeTT\+ |V+#*. d+u$+#& ysDXd+ b]uw+ (technial)>|VseTT n+{sT. >, HsjTD, eVXs d+|H |b~+qe|+&s+.

    nVeT+f @$T{? y |k~++~. y

  • >+y\T>=+yqT&T L& +>, bD jT ysD+ |+|&q~.d+d uw @ jTT ||]o*d n DY... n d+e ns+ Hs+_+q Xd+, eTs\n`n n d+e ns+ |]de|eTeT+~. |Ps+ #|q |Vsd+|
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  • >nq+eTT (Infinity - ) nqT d+K d+u$+| &q~. B yy#yTq |s XeTTqTnq+d+K (Infinity - ) qT *jTCdT+~. |syT nH q|+d*vZyTXsXeTTq d+eTT> #|&q jT+s|yTq eeTT (circle)qT*jTCdT+~. n~ |ssyTq VeTTqT ddT+~. d+UyTq (-Infinity) nq++ L& VeTTH sdT+V+#*.

    |sTwXeTT :` y y#eTTqed+K (9) ddT+~. VyjTq sT qed+K |Dy L&

    30 |PsMTe+k

  • > d+u$d eT+d+Uq+ sdT+~. ~ z+s $wjT+.

    |d]+ n_eeTT y\d+*++~. Vy#yTq d+K (9) > #|H+. 1 qT+& 9 es>\ n+\qT 9 # >TDd ( |jTqT VAsDeT+{sT,) |DeeTT 9eT]jTT nVyT (VeTT) 18 dsD 8 \ d+K s&TsTT. yqT+& eTs\ eT*eTT q 8 n+\T ( 2 qT+& 9 ) d~ksTT. > |d+KjTTq| u>e

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  • > *jTCksTk$TysT.

    n n |eT ys= ns+seTTqTn|dT+~. sTy nq>H |

  • > >V+#*. sseTT L&, |PsXeTTq kse? |s se? nH MTe+d |s syTqd e VyjTq |PsyT ds#eTT\, nq>jT+eTT\{ n~cqeT deT+# e\dq $wjT yTT{ jTTq~. |PseTTqd\ #~cqeT #|q~ d \DyT deT>yTq s#q+ ] `

    ~~jT #|+> >\eTT >V$T~jT #|+> e\qT |&

  • > >V+s s eTT> >V+#*.

  • >#]+#&+dsT\ nqTue >#syTq $wjTyT. ueXeTT\ d+j>eTT e\eTTeT (Optical illusion) eyT. n #q esT seTT e\eTTeqdyTq nqTue q sU s|eT>T eyT. eTTq jTqTueeTTDXd+ $Xw+ $e]++~.eqH k$TysT ` ed nq+sU D |e | c+ keek|q
  • >H nq+ uTeTT\qT DeTT\qT $$ eTT+
  • > (>> &T dueeTT) ( &T dueeTT#) y+&jTHu+ |e $wjT+ d+u$+#& eXeTTq~. $T
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  • > >\|]eyTs&TqT. (+ 6) ~ eeTT +yTq d s| d
  • >+ $#sD |PssTTqT>H u$+|e#TqT.

    @\qq >D XdE&T q |b+$#sDqT eTTd |+#D ||+#eTT e >TDeTT\bXk ddT+~.

    sTy\ >+D, n+>D,|Tq$T (Algebraic, Arithematic, Solid geometrical) $wj\d++~+q $y#q >$+|&q~.

    deTqjTeT+jTT eTq+ |PsdeTT $y+#Tq

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  • >DXdeTTq d++~+ X+e K+&\qT s|+#d+
  • >&q s+&VeTT\ s eTsd |PseTT> eyT nsFjT eTT\ | s|+#T #TqVq @s&T j sFjTeTT\ yH~ ye u
  • > s+ dr]+#&+~.

    eeTT nq+sK\T DeTT\T>\ VQuT> esTssU|]e+> d+u$+|& u$+#&yT? nq+sK\qT DeTT\qT nq+>TDeTT\T> |s=|PseTTqT nq+>TD ]+#&+ ]+~. n+|&T sejT\DyT

  • > |jTT+#Tq~. e]+jTT+&T

    |]sK #|&q~. e]+ jTT+&Tq~ nH | ys= | eTq d+$TdTq ejT V+#*.

    esDX eTq ds|yTq nV+qT nd q HqTqT, $T+,eTs>T|s q

  • >VeTT, VeTT\# eyT esD|]~ V ue'HD e |+# du d#jT+

    n

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  • > #|&q~. (KLMN) e ]wyTq e.1. Xs, 2. eTV_+
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  • > y# yTq V #eTTq, y#yTq|Dy y# y# d++
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    |]DeTk|y eT\ |T\T, y d++~+q$T\ jTT |#j|#jT ` nq> e~jTeTT\T d+u$+#T #TqeueeTT.

    d+U ||+# |+ d+\q, >TD (By Addition and Multiplication)|jT\ e\q e~jTT, ee\q, Vs |jT\ (Substraction andDivision) e\q jTeTT T#Tq$. nf es, |

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  • >Td+uw+#TH|&T |y~ |+# keTT> dsq deTeTT> V seeTV$wjTeTTqT ksueTT> u~+#T ds#q >=|
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  • >seTT&T>H *b&H $wj ~s
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  • > o Nw uo uu o z
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  • > n uw + e]+#sT. ne> n+f CqyT.nTD : TD ) e#T. M{ *dqTD+. \eb sTZD+. +TD+ $u. >TDeT+f n|sT&T. Je&TdeTw Je&T. VTs|T&q >TsTe j>T&q w& #d u sVd yTqV w& nqTu y # |uTV : >TV q~. >| yTq~. sVd +. n{H sVd yTq~.$Cq+. >TV+ V dHq+ nqe. s$TV+ n ^e#qeTT. The top secret n ns+. l\*dVdHe\ |syTX] >TV (653) >| (278)>TVs|D (743) yTT
  • >TDy#eTT. >TDeTTn#qeT>T# TseTT|sTyT#Tq~ nqT nseTT e#TqT.

    V

  • > #d d*$TdT+~. +f
  • >e u>eT L& Quarter nsyT. qT#TcY n e]++~ e+& +. H\T>T bY {. d|+ s+&e~. dTw| eT&e~. bTjTyTq de~ H\T>e~. yTTeT+. n+f #ske~ >eT+. #s& kq+. bMT eyTq ||+#+ . $T> eT&ne+. neT+. Unchanged. |
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  • >VdT&q y&T #d jTC\T nsTT
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