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Category: Math Monday

Category: Math Monday

Last week we showed that YouTube also suffered from the same problem as CTP Teams did a few weeks back when the counter maxed out at 2,147,483,647 and today we will explore the significance of that number a little more.

The problem is actually known as the Y2038 issue because many computers are likely to be affected by this very problem on January 19, 2038 at exactly 3:14:07am GMT.

Basically every computer program which uses a 32-bit signed integer to work out the time using the ‘time()’ function in C/C++, or a similar function in other languages, could be affected.

This is because these programs work out the time by adding up the number of seconds which have passed since January 1, 1970 and 3:14:07am GMT on January 19, 2038 is exactly 2,147,483,647 seconds past that date.

What may happen after this time on non Y2038-compliant systems?

Well like in CTP Teams the counter (clock) may just stop counting or it may begin counting again from the beginning and represent the time as January 1, 1970. It may even take 68 years from the start date and go back to December 1901.

Here is an example of how this may work out in practice:

Year 2038 problem.gif
Year 2038 problem” by MonanekoOwn work. Licensed under Public domain via Wikimedia Commons.

Y2038 does not affect 64-bit computers running 64-bit operating systems and  also does not affect software which does not use time in any way.

However do note that a 64-bit operating system can also run or emulate 32-bit software which may not be Y2038-compliant.

According to the website Y2038.com what is the worst that could happen?

It says: “Electric power plants could go off line. Cars may not start or behave erratically. Global communication could come to a halt. The Internet could entirely or partially stop working. Satellites may cease to function and possibly fall out of orbit. Many embedded devices may malfunction.

“The use of 32-bit time values stored in databases could easily cause a fair amount of confusion until the problems are resolved. Fortunately, there is plenty of time left to mitigate these potential issues.”

Further reading: Y2038.com

 

 

Can you believe that there has actually been a request for a nerdy math post here on CTP Teams? Look I will show you.

Sunny CTP Teams Question

It came from Sunny Suggs after I referred to the sum of the internal angles of a 10-sided polygon in this blog post – What Does 1440 Mean To You?

So let’s get nerdy with some math. Feel free to walk away now if this is of no interest to you because there is nothing but math in this post, although not difficult math.

Let’s take the starting point that the interior angles of a triangle (any triangle) will always add up to 180 degrees. This means that in any given triangle only one of the angles can 90 degrees or greater and in a right angled triangle (where one angle is always 90 degrees) the other two angles must each be 45 degrees.

For some triangle fun – and to prove this for yourself then click on the image below and have a little play with the graphic to move the triangle and see what happens to its angles. (It will open up in a new tab so don’t forget to come back here when you are done playing.)

Interior angles of a triangle
Next up, a four sided shape or quadrilateral (such as a square or rectangle) is able to be cut in to two triangles so it follows that its internal angles must add up to 360 degrees, (180 + 180 degrees.)

In addition if the quadrilateral is one where all four vertices lie on a circle, known as a cyclic or inscribed quadrilateral, then each pair of opposite interior angles will always add up to 180 degrees. Again, click on the image below to find out for yourself.

interior angles of a quadrilateral

A five-sided shape, called a pentagon, can be cut into three triangles so its interior angles must add up to 3 x 180 = 540 degrees. A six sided polygon, a hexagon, can be cut into four triangles so its interior angles must add up to 4 x 180 = 720 degrees.

So from this pattern we can work out a formula to find the sum of the internal angles of any polygon, thus:

where the number of sides on the polygon = n then the sum of that polygon’s internal angles will be sum = 180 x (n-2) degrees.

So the sum of the internal angles of a 10-sided polygon must be

180 x (10-2) degrees

= 180 x 8 degrees

= 1440 degrees which is the figure given in the original blog post.

Finally if you want to play with some more polygons then click on this link below.

Sum of internal angles in any polygon

All graphic images used in this post are from Math Open Reference.