Could Someone give me a link to this pdf:
An Introduction to Projective Geometry by Bobby Poon
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- Thu Dec 12, 2013 6:29 pm
- Forum: Geometry
- Topic: Projective Geo PDF
- Replies: 0
- Views: 1500
- Thu Dec 12, 2013 5:49 pm
- Forum: Higher Secondary Level
- Topic: dividing $x^{2013}-1$
- Replies: 7
- Views: 6896
Re: dividing $x^{2013}-1$
Sorry...
- Sun Oct 13, 2013 5:58 pm
- Forum: Higher Secondary Level
- Topic: dividing $x^{2013}-1$
- Replies: 7
- Views: 6896
Re: dividing $x^{2013}-1$
Let, $\mathcal{P}(x)=x^{2013}-1$. Also, suppose, when $\mathcal{P}(x)$ is divided by $(x^2+1)(x^2+x+1)$, the remainder is $\mathcal{R}(x)$. So, $\mathcal{R}(x)$ is a 3-Degree polynomial. [$\because (x^2+1)(x^2+x+1)$ is a 4-Degree polynomial.] So, $\mathcal{P}(x)=(x^2+1)(x^2+x+1)\mathcal{Q}(x)+\mathc...
- Sun Oct 13, 2013 4:49 pm
- Forum: Geometry
- Topic: Geometry book recommendation
- Replies: 2
- Views: 4830
Re: Geometry book recommendation
Well, there's always "GEOMETRY REVISITED". But, if web-resources work for you, then, :arrow: Forum Geometricorum : A geometry journal which covers many topics on the recent developments of Euclidean Geometry. :arrow: Cut-The-Knot : A website with a very rich Geometry Section. It features many articl...
- Sun Sep 08, 2013 7:40 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Higher Secondary 8
- Replies: 6
- Views: 6233
Re: BdMO 2013 Higher Secondary Problem 8
$X,A,Y,C$ is Cyclic $\Rightarrow EA.EC=EX.EY$ ; $X,S,Y,Z$ is Cyclic $\Rightarrow EX.EY=ES.EZ$. So, $EA.EC=ES.EZ.....(1)$ Again, the Pencil of Rays $B(Z,C,E,A)$ is Harmonic. So, $\displaystyle \frac{EA}{EC}=\frac{ZA}{ZC}.....(2)$ Using relation $(1)$ & $(2)$, we can deduce that, $SC=2AC$. So, $S$ is ...
- Wed Feb 06, 2013 11:20 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2012: Primary 4
- Replies: 8
- Views: 7773
Re: BdMO National 2012: Primary 4
@famim2011: $98886$ is also a beautiful, but, it's not the largest. $99866$ is the largest.
- Wed Feb 06, 2013 8:45 pm
- Forum: Divisional Math Olympiad
- Topic: Some problems of last year divisionals, I need help for
- Replies: 36
- Views: 20529
Re: Some problems of last year divisionals, I need help for
Suppose, $D$ is your required point. It lies on the semi-circle on $BC$ ( why? ), and, $AC$ is tangent to it. Then, $\angle DCA=\angle DBC$ (Tangent-Chord Theorem). So, $\angle EBD=\angle DBC$, which implies, $BD$ is the Angle-Bisector of $\angle ABC$. From this, it follows, $\angle EBC=\angle ECB=6...
- Wed Feb 06, 2013 12:07 pm
- Forum: Combinatorics
- Topic: Sum
- Replies: 7
- Views: 6678
Re: Sum
I am guessing, $n\in\mathbb{N}$....
Re: TARZAN
@ SMMamun : I think you are having trouble to see the whole picture here. Suppose, Tarzan and the bullet are in space, and, the given scenario occurs, without any reference point in their vicinity, other than themselves. The only form of motion in them are the vertical acceleration of Tarzan and the...
- Thu Jan 17, 2013 8:59 pm
- Forum: Higher Secondary Level
- Topic: A Differentiation Dilemma
- Replies: 1
- Views: 2659
A Differentiation Dilemma
Let, $f(x)=x^2$. So, $\displaystyle f'(x)=\frac{\mathrm {d}}{\mathrm {d}x} \big( f(x) \big)=\frac{\mathrm d}{\mathrm dx}(x^2)=2x$. Again, \[\displaystyle f(x)=x^2=x\times x=\underbrace{x+x+x+\ldots+x}_{x\,\text{times}}\] Therefore, \[\displaystyle f'(x)=\frac{\mathrm {d}}{\mathrm{d}x}\big(f(x)\big)\...