<p>5^2 is gone, but lurkers are in luck. 29 is coming up, and, as mruncleramos noted, 28 would simply be perfect as well!</p>
<p>Did anyone notice that the probability of being a prime or a perfect square in first 30 places = .5? Maybe we just consist of the people who are not unlucky.</p>
<p>I don't see what's so great about perfect squares. They don't seem very interesting to me. The only ones that are mildly interesting are the squares of primes, but all the other ones have no randomness or anything like that to them.</p>
<p>hes just jealous because he didnt sign up in time to get one</p>
<p>hahahahaha maybe thats true. But I'm wondering, sonar, why do you like perfect squares so much?</p>
<p>I'm not sonar, but I like perfect squares too. When I was younger, this formula fascinated me:</p>
<p>1^2+2^2+...+n^2 = n(n+1)(2n+1)/6</p>
<p>It has at least 5 different proofs, including an awesome double-counting proof.</p>
<p>Also interesting is the sum of reciprocals of primes:</p>
<p>1/1^2 + 1/2^2 + 1/3^2 + ... = pi^2/6</p>
<p>And heres my favorite two problems involving squares:</p>
<p>If k<em>1<k</em>2<k<em>3<... are positive integers, no two consecutive and s</em>m=k<em>1+k</em>2+...+k<em>m. Prove that for every positive integer n, the interval [s</em>n,s_(n+1)) contains at least one perfect square.</p>
<p>Let a<em>1,a</em>2,...,a_n, (n>3) be reals so </p>
<p>a<em>1+a</em>2+...+a<em>n >= 2 and a^2</em>1 + a^2<em>2 + ... + a^2</em>n >= n^2. </p>
<p>Prove that the largest of a<em>1,a</em>2,...,a_n is greater than or equal to 2.</p>
<p>But cubes are pretty cool too - the sum of the first n cubes is equal to the square of the sum of the first n numbers.</p>
<p>"Also interesting is the sum of reciprocals of primes:</p>
<p>1/1^2 + 1/2^2 + 1/3^2 + ... = pi^2/6"</p>
<p>^^ that's the sum of the reciprocals of the squares of the natural numbers, not primes. the sum of the reciprocals of the squares of the primes converges to 0.4522474200410654985065</p>
<p>...and the sum of the reciprocals of primes diverges</p>
<p>ughhh thats what i meant tsr472.... lol</p>
<p>I should have just said Zeta(2) = pi^2/6.</p>
<p>haha, I was confused when I first read that tetrahedr0n.</p>
<p>Yeah, the sum of squares is cool, but as is the relation between squares and triangular numbers. Though, that one may just be me.</p>
<p>yeah..."the sum of the reciprocals of the squares of the primes converges to 0.4522474200410654985065" is really wordy...I think it's the same as primeZeta(2)=0.4522474200410654985065</p>
<p>I'm surprised. I really thoguht that as many as 60-70 CCers would have applied and added their names to the roster. Do you suppose there are a lot of applicants who are too nervous to list themselves?</p>
<ol>
<li>AltairAqua/ Biology: virology; Chemistry: organic/ LA</li>
<li>huangm/ Physics: nanotech; Mathematics: discrete math</li>
<li>Dmitriy_Y/ Engineering: mechanical engineering(robotics); physics: theoretical astrophysics / NJ / 800m 700v</li>
<li>New Yorker/ Psychology: cognitive neuroscience; Political Science: political behavior & socialization/ NY</li>
<li>schemer/ Computer Science : programming languages; Computer Science : theory & algorithms/ NY
6.Random^4/Physics : Cosmology; Physics : Astronomy/MN</li>
<li>Pygo/ Biology : marine; Chemistry : marine/ RI</li>
<li>tsr472/ Math: mathematical physics; Math: Set Theory (Order & Lattice Theory) / AR</li>
<li>tetrahedr0n/Math: combinatorial game theory; Math: additive number theory</li>
<li>ReasonableSon/ Computer Science: AI; Computer Science: Robotics / PA</li>
<li>smurf816/ Physics: quantum mechanics; Bio: biotechnology</li>
<li>mruncleramos/ Mathematics: Differential Geometry/Topology; Physics: Gravitational Waves and Singularities</li>
<li>intelliot / Computer Science: Search Algorithms; Engineering: Digital Signal Processing</li>
<li>kinglz/ Molecular Biology: Chaperones and protein transport; Molecular Biology: Neurodegenerative Diseases</li>
<li>Frankthetank314159/ Engineering: nano; Physics: optics, preferably holography, because holography is cool.</li>
<li>dualityim/Biology: Biochemistry; Computer Science: Computer Architecture.</li>
<li>DanHak/Physics: Particle Physics; Physics: Astrophysics (PSAT: 77V, 73M)</li>
<li>maverick27/Nanotech: Nanomaterials (organic membranes); Physics: Elementary particles/NJ.</li>
<li>sonar/Mathematics: Knot Theory; Computer Science: Optimization</li>
<li>puddinggirl/Chemistry: organic; Biology: biochemistry (SAT 790M 800V)</li>
<li>ccerforlife/Mathematics: Foundations of Geometry in the Non-Euclidean Plane and with Limited Axioms; Mathematics: Number Theory (in systems lacking induction)</li>
<li>adidasty/Biology: Cellular/Molecular Biology; Mathematics: Applied Math/Data Analysis (780M 690V, 76M 77W 63CR, 800 BioE/M)</li>
<li>ArmenianInvasion: Engineering, Mechanical; Chemistry, Materials/Nanotechnology - reppin the MD</li>
<li>sarkun: Engineering-neuroengineering brain computer interphases in particular- Engineering-robotics US citizen living in Turkey so have no idea as to how I will be considered </li>
<li>outlier/ Biology: Molecular; Engineering: Biomedical</li>
<li>wishful_thinker/ Engineering: Biomedical, Biology: Genetics</li>
<li>Tero771/ Neuroscience: Molecular and Cellular, Biology: Immunology</li>
</ol>
<ol>
<li>AltairAqua/ Biology: virology; Chemistry: organic/ LA</li>
<li>huangm/ Physics: nanotech; Mathematics: discrete math</li>
<li>Dmitriy_Y/ Engineering: mechanical engineering(robotics); physics: theoretical astrophysics / NJ / 800m 700v</li>
<li>New Yorker/ Psychology: cognitive neuroscience; Political Science: political behavior & socialization/ NY</li>
<li>schemer/ Computer Science : programming languages; Computer Science : theory & algorithms/ NY
6.Random^4/Physics : Cosmology; Physics : Astronomy/MN</li>
<li>Pygo/ Biology : marine; Chemistry : marine/ RI</li>
<li>tsr472/ Math: mathematical physics; Math: Set Theory (Order & Lattice Theory) / AR</li>
<li>tetrahedr0n/Math: combinatorial game theory; Math: additive number theory</li>
<li>ReasonableSon/ Computer Science: AI; Computer Science: Robotics / PA</li>
<li>smurf816/ Physics: quantum mechanics; Bio: biotechnology</li>
<li>mruncleramos/ Mathematics: Differential Geometry/Topology; Physics: Gravitational Waves and Singularities</li>
<li>intelliot / Computer Science: Search Algorithms; Engineering: Digital Signal Processing</li>
<li>kinglz/ Molecular Biology: Chaperones and protein transport; Molecular Biology: Neurodegenerative Diseases</li>
<li>Frankthetank314159/ Engineering: nano; Physics: optics, preferably holography, because holography is cool.</li>
<li>dualityim/Biology: Biochemistry; Computer Science: Computer Architecture.</li>
<li>DanHak/Physics: Particle Physics; Physics: Astrophysics (PSAT: 77V, 73M)</li>
<li>maverick27/Nanotech: Nanomaterials (organic membranes); Physics: Elementary particles/NJ.</li>
<li>sonar/Mathematics: Knot Theory; Computer Science: Optimization</li>
<li>puddinggirl/Chemistry: organic; Biology: biochemistry (SAT 790M 800V)</li>
<li>ccerforlife/Mathematics: Foundations of Geometry in the Non-Euclidean Plane and with Limited Axioms; Mathematics: Number Theory (in systems lacking induction)</li>
<li>adidasty/Biology: Cellular/Molecular Biology; Mathematics: Applied Math/Data Analysis (780M 690V, 76M 77W 63CR, 800 BioE/M)</li>
<li>ArmenianInvasion: Engineering, Mechanical; Chemistry, Materials/Nanotechnology - reppin the MD</li>
<li>sarkun: Engineering-neuroengineering brain computer interphases in particular- Engineering-robotics US citizen living in Turkey so have no idea as to how I will be considered </li>
<li>outlier/ Biology: Molecular; Engineering: Biomedical</li>
<li>wishful_thinker/ Engineering: Biomedical, Biology: Genetics</li>
<li>Tero771/ Neuroscience: Molecular and Cellular, Biology: Immunology</li>
<li> mobius27 Nano: apps in biological sciences, Bio: genetic manipulation</li>
</ol>
<p>"Do you suppose there are a lot of applicants who are too nervous to list themselves?" Yes, probably tons of them. As you can see, two entries were just added, in less than two hours.</p>
<ol>
<li>AltairAqua/ Biology: virology; Chemistry: organic/ LA</li>
<li>huangm/ Physics: nanotech; Mathematics: discrete math</li>
<li>Dmitriy_Y/ Engineering: mechanical engineering(robotics); physics: theoretical astrophysics / NJ / 800m 700v</li>
<li>New Yorker/ Psychology: cognitive neuroscience; Political Science: political behavior & socialization/ NY</li>
<li>schemer/ Computer Science : programming languages; Computer Science : theory & algorithms/ NY
6.Random^4/Physics : Cosmology; Physics : Astronomy/MN</li>
<li>Pygo/ Biology : marine; Chemistry : marine/ RI</li>
<li>tsr472/ Math: mathematical physics; Math: Set Theory (Order & Lattice Theory) / AR</li>
<li>tetrahedr0n/Math: combinatorial game theory; Math: additive number theory</li>
<li>ReasonableSon/ Computer Science: AI; Computer Science: Robotics / PA</li>
<li>smurf816/ Physics: quantum mechanics; Bio: biotechnology</li>
<li>mruncleramos/ Mathematics: Differential Geometry/Topology; Physics: Gravitational Waves and Singularities</li>
<li>intelliot / Computer Science: Search Algorithms; Engineering: Digital Signal Processing</li>
<li>kinglz/ Molecular Biology: Chaperones and protein transport; Molecular Biology: Neurodegenerative Diseases</li>
<li>Frankthetank314159/ Engineering: nano; Physics: optics, preferably holography, because holography is cool.</li>
<li>dualityim/Biology: Biochemistry; Computer Science: Computer Architecture.</li>
<li>DanHak/Physics: Particle Physics; Physics: Astrophysics (PSAT: 77V, 73M)</li>
<li>maverick27/Nanotech: Nanomaterials (organic membranes); Physics: Elementary particles/NJ.</li>
<li>sonar/Mathematics: Knot Theory; Computer Science: Optimization</li>
<li>puddinggirl/Chemistry: organic; Biology: biochemistry (SAT 790M 800V)</li>
<li>ccerforlife/Mathematics: Foundations of Geometry in the Non-Euclidean Plane and with Limited Axioms; Mathematics: Number Theory (in systems lacking induction)</li>
<li>adidasty/Biology: Cellular/Molecular Biology; Mathematics: Applied Math/Data Analysis (780M 690V, 76M 77W 63CR, 800 BioE/M)</li>
<li>ArmenianInvasion: Engineering, Mechanical; Chemistry, Materials/Nanotechnology - reppin the MD</li>
<li>sarkun: Engineering-neuroengineering brain computer interphases in particular- Engineering-robotics US citizen living in Turkey so have no idea as to how I will be considered </li>
<li>outlier/ Biology: Molecular; Engineering: Biomedical</li>
<li>wishful_thinker/ Engineering: Biomedical, Biology: Genetics</li>
<li>Tero771/ Neuroscience: Molecular and Cellular, Biology: Immunology</li>
<li>mobius27 Nano: apps in biological sciences, Bio: genetic manipulation</li>
<li>Spydertennis Biology; Neuro / Biotech; Nanotech</li>
</ol>
<p>you know what, lets just say that all the people on this list got in. theres still a good 40 spots out there for people who didn't list :)</p>
<p>here's a question,
how many people have done actual research work in the topic they specified?</p>
<p>I have. </p>
<p>How about you?</p>
<p>mobius27, how many people will be accepted to RSI? 69 (29+40)?</p>
<p>"how many people have done actual research work in the topic they specified?"</p>
<p>i did some last summer</p>
<p>Same here, last summer.</p>