# Easing functions for your animations

Today’s design guidelines state that all animated movement inside your application should contain so called easing. You can read this section from google material design. If your UI-framework does not contain implementations for standard set of easings you can create your own.

Here is place where you can check out animated plottings for basic easing functions. And here you can find source code for them in several languages (JS,Java,Lua,C#,C++,C).

# Beal prize – first approach

May be you already heard that so called Beal Prize was increased to 1.000.000\$ (http://ns3.ams.org/bealprize.html). So if you can find positive integers A^x+B^y=C^z where x,y,z > 2 and A,B,C dont have common factor, you can get a lot of cash. As you can see its not a complication to write a piece of code to check some range of numbers, or generator to generate some lucky numbers. Its officially checked only in range where all numbers are less than 1000.

So i decided to try my luck.

As first approach i decided to generate a lot of prime numbers (15.000.000 for start). This is C++ code for relatively fast generation of prime numbers:

// Primes

int MAXPRIME = 15000000;

unsigned long * primeNumbers = new unsigned long[MAXPRIME];

LOG << “Computing “ << MAXPRIME << ” prime numbers…” << NL;

LOG.startProfile();

{

long x = 3;

long sqrtIndex = 0;

for (int i = 2; i < MAXPRIME; i++)

{

bool ok = false;

while (!ok)

{

x += 2;

if ((x % 6 == 1) || (x % 6 == 5))

{

ok = true;

sqrtIndex++;

for (int j = 0; j <= sqrtIndex; j++)

if (x % primeNumbers[j] == 0)

{ ok = false; break; }

}

}

if (i % 100000 == 0)

LOG << i << ” [ “ << primeNumbers[i] << ” ] “ << NL;

}

}

LOG.profile(“Computing “ + SS::toString(MAXPRIME) + ” prime numbers was completed”);

To check Beal conjecture we need support of very long integers for C++. I have my own implementation, but you can use any decent library.As first straight-forward approach i decided to do in endless cycle the following (until i get lucky numbers):

• Get two random prime numbers from pregenerated array.
• Generate random x,y,z within reasonable range.
• Compute S=A^x+B^Y
• Compute the most close C – which gives (2*C)^z ~ S (i have used simple method of bisection).
• If (2*C)^z == S break and report success.

I got yet no success, and some mathematicians tell that conjecture is probably true. But still why not to try to search if it is so easy.