• ### Solving Buffering Nightmare Mathematically?

A typical YouTube SD video with 480p quality has an average bit rate of 1200 kbps (kilo bits per second). Mr X's internet connection has speed of 512 kbps. If Mr. X decides to watch a 60 minute video on YouTube, find minimum time in seconds he should allow buffering so that he can watch the video uninterrupted.
A typical YouTube SD video with 480p quality has an average bit rate of 1200 kbps (kilo bits per second). Mr X's internet connection has speed of 512 kbps. If Mr. X decides to watch a 60 minute video on YouTube, find minimum time in seconds he should allow buffering so that he can watch the video uninterrupted.
1 answer · Mathematics · 4 years ago
• ### Creating Sphere from 3D Spirals?

Recently during my travel I stumbled upon this vessel (as shown in pic) which is used for keeping holy water. As can be seen from image it contains two interwoven 3D spirals (one golden and other black). Questions: (1) Is is fair to assume that such spirals can be used to create complete sphere? (2) Define mathematical functions that governs such... show more
Recently during my travel I stumbled upon this vessel (as shown in pic) which is used for keeping holy water. As can be seen from image it contains two interwoven 3D spirals (one golden and other black). Questions: (1) Is is fair to assume that such spirals can be used to create complete sphere? (2) Define mathematical functions that governs such 3D spirals?
1 answer · Mathematics · 4 years ago
• ### String of 1s and Prime numbers?

Prove that if (10^n-1)/9 = Prime then 'n' is also a prime number.
Prove that if (10^n-1)/9 = Prime then 'n' is also a prime number.
2 answers · Mathematics · 5 years ago
• ### Realtime content grabbing:How will you use it?

Recently through stumble upon I found "Wepware", a new google chrome extension. The cool part in my opinion about that extension is ability to capture any part of the website, and when you open that grab it shows realtime content of that relevant part only. you can see this video to understand what I am referring... show more
Recently through stumble upon I found "Wepware", a new google chrome extension. The cool part in my opinion about that extension is ability to capture any part of the website, and when you open that grab it shows realtime content of that relevant part only. you can see this video to understand what I am referring to: http://www.youtube.com/watch?v=pvTanWngk... Poll: How will you use this type of functionality?
2 answers · Polls & Surveys · 5 years ago
• ### Bullet Block Experiment?

Have a look at the following video http://www.youtube.com/watch?v=vWVZ6APXM... What do you think is the reason? I think angular momentum helps it to maintain the same course (same as the one hit in the middle) and hence displacement is constant. I may be completely wrong but that is what I think. ;)
Have a look at the following video http://www.youtube.com/watch?v=vWVZ6APXM... What do you think is the reason? I think angular momentum helps it to maintain the same course (same as the one hit in the middle) and hence displacement is constant. I may be completely wrong but that is what I think. ;)
5 answers · Physics · 5 years ago
• ### Mysterium Cosmographicum : Redux?

In his famous work "Mysterium Cosmographicum" Kepler proposed a three dimensional model based on nested Platonic solids to explain the mainly two dimensional planetary orbital motions. Refer to the image below: http://chapin.williams.edu/pasachoff/graphics/Kepler%20Mysterium%20plate%203.jpg Question (of course this has nothing to do... show more
In his famous work "Mysterium Cosmographicum" Kepler proposed a three dimensional model based on nested Platonic solids to explain the mainly two dimensional planetary orbital motions. Refer to the image below: http://chapin.williams.edu/pasachoff/gra... Question (of course this has nothing to do with Kepler's work) : If the five platonic solids Tetrahedron, Cube, Octahedron, Dodecahedron and Icosahedron respectively (in that order) are packed inside spheres of optimum radius (i.e. most efficient packing) and if the length of side of Tetrahedron is 1 unit (which is the innermost platonic solid), find out the radius of outermost Sphere. To avoid any misunderstanding, the configuration goes like this: Firstly a Tetrahedron of unit side length is packed inside a sphere, which is inside a Cube packed inside a sphere, which is again inside a Octahedron packed inside a sphere, and so on.. . . this ends which a Icosahedron being packed inside a sphere.
1 answer · Mathematics · 5 years ago
• ### Resonance and its Math?

Checkout the following video http://www.youtube.com/watch?v=1yaqUI4b9... Since we know frequency of each configuration, is there any way that we can find mathematical equation for a given configuration at a particular frequency? For example what is the underlying function to the first configuration appearing at 15th second of the video at 368hz?
Checkout the following video http://www.youtube.com/watch?v=1yaqUI4b9... Since we know frequency of each configuration, is there any way that we can find mathematical equation for a given configuration at a particular frequency? For example what is the underlying function to the first configuration appearing at 15th second of the video at 368hz?
3 answers · Mathematics · 5 years ago
• ### Precious Primes : Find Next one?

A prime number "P" is a Precious Prime of Order "N" if Σ Prime(i)^n (where Prime(i)=2 to P) is also a prime for all n = 1 to N Let's take some example: 3 is a precious prime of order 2 because 2^2 + 3^2 = 13 which is a prime and 2^1+3^1=5 which is also a prime. Like that 33773 is a precious prime of order 4 because... show more
A prime number "P" is a Precious Prime of Order "N" if Σ Prime(i)^n (where Prime(i)=2 to P) is also a prime for all n = 1 to N Let's take some example: 3 is a precious prime of order 2 because 2^2 + 3^2 = 13 which is a prime and 2^1+3^1=5 which is also a prime. Like that 33773 is a precious prime of order 4 because 2^1 + 3^1 + 5^1 + 7^1 + 11^1 + . . . . . + 33773^1 = 57 584 381 which is a prime 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + . . . . . + 33773^2 = 1 276 400 440 541 which is also a prime 2^3 + 3^3 + 5^3 + 7^3 + 11^3 + . . . . . + 33773^3 = 32 129 765 754 996 971 which is also a prime 2^4 + 3^4 + 5^4 + 7^4 + 11^4 + . . . . . + 33773^4 = 865 842 131 651 904 557 537 which is also a prime Question: Find next such Precious Prime of order 4. BTW I really doubt if we can have precious primes of order higher than 4 :)
1 answer · Mathematics · 5 years ago
• ### In search of NPP - Non-Perfect Primes?

Let PP denote sequence of perfect prime numbers which are derived from [pq mod (p+q)] where p & q both are prime numbers. For instance for p =2 and q=5 we have PP = (2*5) mod (2+5) = 3 which is a prime number so 3 is PP. Similarly for p=83 and q=71 we have PP = 5893 mod 154 = 41 which is again a prime number so 41 is also PP. There are many... show more
Let PP denote sequence of perfect prime numbers which are derived from [pq mod (p+q)] where p & q both are prime numbers. For instance for p =2 and q=5 we have PP = (2*5) mod (2+5) = 3 which is a prime number so 3 is PP. Similarly for p=83 and q=71 we have PP = 5893 mod 154 = 41 which is again a prime number so 41 is also PP. There are many such examples. Can you find NPP i.e. sequence of Non Perfect Prime numbers (numbers that can not be derived from prime numbers as discussed above) ?
5 answers · Mathematics · 5 years ago
• ### Infinitely Inscribed Regular Polygons?

Let S(n) (where n > 2) represented sum of the areas of 'n' sided regular polygon which are infinitely inscribed within each other where largest polygon has side length of 1 unit. Refer to the following image http://aiminghigh.aimssec.org/wp-content/uploads/2012/01/7squares.gif It shows inscribed squares and we know that S(4) = 2... show more
Let S(n) (where n > 2) represented sum of the areas of 'n' sided regular polygon which are infinitely inscribed within each other where largest polygon has side length of 1 unit. Refer to the following image http://aiminghigh.aimssec.org/wp-content... It shows inscribed squares and we know that S(4) = 2 which is convergent. I believe at certain large 'n', S(n) becomes divergent or at least inconclusive. Question: At what 'n', S(n) becomes divergent? What are your thoughts on S(n)?
3 answers · Mathematics · 5 years ago
• ### Prime Number and Sum of Digits?

Let p represent a prime number and sd(p) denote sum of digits of 'p'. Let S(n) represent sequence where [p^sd(p)+1] = 0 mod sd(p) S(n) = 11, 37, 73, 101, 127, 163, 223, 263, 307, 337 . . . Is there any way to define S(n) in any other terms or is there a way to find 'n'th term directly? Are there any interesting characteristics... show more
Let p represent a prime number and sd(p) denote sum of digits of 'p'. Let S(n) represent sequence where [p^sd(p)+1] = 0 mod sd(p) S(n) = 11, 37, 73, 101, 127, 163, 223, 263, 307, 337 . . . Is there any way to define S(n) in any other terms or is there a way to find 'n'th term directly? Are there any interesting characteristics of this sequence?
1 answer · Mathematics · 5 years ago
• ### Abundant Numbers Question?

In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. What is the probability of a randomly selected number being (1) an Abundant Number (2) an Odd Abundant Number
In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. What is the probability of a randomly selected number being (1) an Abundant Number (2) an Odd Abundant Number
4 answers · Mathematics · 5 years ago
• ### Celebrating Prime Day?

Do you know that 23-March-2013 or 2332013 is a prime day. So let's celebrate it with the following question. Let S denote sum of squares of first n primes. Prove that for n>1, S can not be a square.
Do you know that 23-March-2013 or 2332013 is a prime day. So let's celebrate it with the following question. Let S denote sum of squares of first n primes. Prove that for n>1, S can not be a square.
4 answers · Mathematics · 5 years ago

(1) A sequence {R} of rectangles is generated as shown in the image below. http://farm9.staticflickr.com/8088/8557307742_ed6ee8be95_z.jpg We begin with a unit square R₀ and adjoin the rectangle, of unit area on one SIDE to produce R₁. Then a a next step we adjoin the rectangle of unit area on TOP of the R₁ to produce R₂. If we continuously... show more
(1) A sequence {R} of rectangles is generated as shown in the image below. http://farm9.staticflickr.com/8088/85573... We begin with a unit square R₀ and adjoin the rectangle, of unit area on one SIDE to produce R₁. Then a a next step we adjoin the rectangle of unit area on TOP of the R₁ to produce R₂. If we continuously follow this process on side & top respectively of the previous figure, the ratio of length to height of the rectangle will converge to ______ ? (2) ∏ (n=1 --> ∞) 4n²/(4n²-1) = _____ ? Please answer these questions by tomorrow, otherwise there will be no fun ;-)
6 answers · Mathematics · 5 years ago
• ### Understanding Light a different way?

Have a look at following image: http://farm9.staticflickr.com/8516/8537873172_b30129d5d8_b.jpg The image shows top pose of a box with mirror arrangement (red line indicates reflectors) (1) In the first arrangement will the light will ever come out (i.e. will it come out from the entry point or will it bounce back forever inside. In case someone... show more
Have a look at following image: http://farm9.staticflickr.com/8516/85378... The image shows top pose of a box with mirror arrangement (red line indicates reflectors) (1) In the first arrangement will the light will ever come out (i.e. will it come out from the entry point or will it bounce back forever inside. In case someone is able to build a perfect infinite reflector what kind or image / scene will appear when someone from top looks at one of the reflectors? (2) For an arrangement shown in the right hand side of the image,what results one will get if someone conducted double split experiment in that? This is something I am very curious about, hope someone can help :)
1 answer · Physics · 5 years ago
• ### Concatenating Consecutive Prime Squares?

Consider a number (N) generated using concatenating squares of consecutive primes. N = (P₁)² (P₂)² (P₃)² . . . . . .(Pk)^2 Easy Question: For what values of "k" , "N" will always be a composite number? Why? Tough Question: For k = 2, is there a simple way/logic to determine whether N is a prime number?
Consider a number (N) generated using concatenating squares of consecutive primes. N = (P₁)² (P₂)² (P₃)² . . . . . .(Pk)^2 Easy Question: For what values of "k" , "N" will always be a composite number? Why? Tough Question: For k = 2, is there a simple way/logic to determine whether N is a prime number?
3 answers · Mathematics · 6 years ago
• ### In Search of the Sandwich numers?

A number is called Sandwich Number if its neighbors are power numbers. i.e. "n" can be considered as Sandwich Number if n-1 and n+1 can be written in form of a^b. From Fermat's Sandwich Theorem we know that 26 is the only number which comes in between square and a cube. i.e. 5^2 & 3^3. Can you find any other?
A number is called Sandwich Number if its neighbors are power numbers. i.e. "n" can be considered as Sandwich Number if n-1 and n+1 can be written in form of a^b. From Fermat's Sandwich Theorem we know that 26 is the only number which comes in between square and a cube. i.e. 5^2 & 3^3. Can you find any other?
4 answers · Mathematics · 6 years ago
• ### Prove that last digit of n^n can never be 2 or 8?

2 answers · Mathematics · 6 years ago
• ### Folding problem (redux)?

Refer to the following question (and diagram) recently asked by falzoon http://answers.yahoo.com/question/index?qid=20130103170147AAQfUOl Now imagine that in the picture you do not divide the square in three equal areas but you draw three parallel lines such that point A coincides with point G. Point B is on line CF and Point C is on line... show more
Refer to the following question (and diagram) recently asked by falzoon http://answers.yahoo.com/question/index?... Now imagine that in the picture you do not divide the square in three equal areas but you draw three parallel lines such that point A coincides with point G. Point B is on line CF and Point C is on line DE. Questions: (1) Is it possible to have such arrangement with a square? If yes, What is the distance between three segments? (2) If this can be done only with rectangle then what is the dimension of such rectangle?
1 answer · Mathematics · 6 years ago
• ### For a & b that are relatively prime If (a^n+b^n)/(a+b) is a prime then n is also a prime.?

Show that, For positive integers a & b that are relatively prime If (a^n+b^n)/(a+b) is a prime then "n" is also a prime.
Show that, For positive integers a & b that are relatively prime If (a^n+b^n)/(a+b) is a prime then "n" is also a prime.
1 answer · Mathematics · 6 years ago