Skip to main content

area of sphere




Well ever wondered how the Surface Area of a Sphere was derived?
Well here is a great visualisation to alter your perception.
Step 1: Cut the sphere in the following way.
Step 2: Spread the cut out part across the paper
Step 3: Collate the pieces together in the following way
Step 4: Spread the areas out separately to form a sine curve
Step 5: The area of the sine curve is the surface area of the sphere
Here’s a GIF file for better understanding.
There’s of course the generic method of calculation where the surface area is calculated by cutting the sphere into infinitesimally thin disks of varying radius stacked over one another and integrating them, but this above method is a different way to look at the same problem.
Image Source: Google Images

220 Loves 284.
Yes, this pair of numbers was considered as a symbol of love in medieval period, lovers used to send flowers, fruits to each other with these numbers written. Also some Arab writings say that couples used to eat apples with these numbers written and believed that it increases their affection and seduces them.
These are called amicable numbers, a pair of numbers, each of which is the sum of the factors of the other. The smallest pair of amicable numbers is (220, 284). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.[1]
The first ten amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368), (10744, 10856), (12285, 14595), (17296, 18416), (63020, 76084), and (66928, 66992)[2]
Thanks for reading!
Footnotes
Labels:

Comments

Post a Comment

Popular posts from this blog

how is tan (A+B) = [tan A + tan B]/[1 - tan A tan B]?

How is tan (A+B) = [tan A + tan B]/ [1 - tan A tan B]? Method 1: Let A = 30 deg and B = 45 deg. LHS = tan (30+45) = tan 75 = 3.732050808 RHS = [tan A + tan B]/[1 - tan A tan B] = [tan 30 + tan 45]/[1 - tan 30 tan 45] = [0.577350269 + 1]/[1 - 0.577350269*1] = 1.577350269/0.42264973 = 3.732050808 = LHS Proved. Method 2: tan (A+B) = [tan A + tan B]/[1 - tan A tan B] RHS = [tan A + tan B]/[1 - tan A tan B] =[(sin A/cos A) + (sin B/cos B)]/[1-(sin A/cos A)(sin B/cos B) = [sin A cos B + cos A sin B]/[cos A cos B][1 - sin A sin B/(cos A cos B)] = sin (A+B)/{[cos A cos B][cos A cos B - sin A sin B]/(cos A cos B)} = sin (A+B)/[cos A cos B - sin A sin B = sin (A+B)/cos (A+B) = tan (A+B) = LHS. Proved. Thanks. source:Quara
Post a Comment
Read more

What are some mind-blowing facts about mathematics?

Prime Generating Polynomials : The polynomial,  n 2 + n + 41 n 2 + n + 41  can be used to produce 40 primes for consecutive integer values 0≤n≤39.  This property was discovered by Euler . Similarly, the incredible formula,  n 2 − 79 n + 1601 n 2 − 79 n + 1601  was discovered, which produces 80 primes for the consecutive values 0≤n≤79! Kaprekar’s Constant : 6174 is known as Kaprekar’s Constant , after the Indian Mathematician D.R. Kaprekar. Take any four-digit number, using at least two different digits (Leading zeros are allowed.) Arrange the digits in descending and then in ascending order, to get two four-digit numbers, adding leading zeroes if necessary. Subtract the smaller number from the larger number and go back to step 2. The above process will always reach the fixed number, 6174, taking at most 7 iterations. Try it yourself! ( Note that after the first subtraction or the subsequent subtractions, the result obtained is always a multi...
Post a Comment
Read more

What is the application of linear equations in two variables in daily life?

In life X = our happiness, life, dreams, desires etc Y = caring for others, other's happiness, value we give to others. In daily life X + Y = Compromise, sacrifice, adjustments but still maintaining happiness of X & Y factors. Stay happy stay blessed Thank you  They are used in solving linear inequalities, which are then used to solve linear programming problems. Now, linear programming, as widely known solves problems about many situations in daily life. It helps you know which food products to buy for requisite nutrition at the least cost, how to travel max. distance in least fuel, how to price your products for a max. profit, and many more
Post a Comment
Read more