Happy New Year!πŸ₯‚πŸŽ‰πŸŽ‡ The maths of fireworks and leap years πŸ‘€

It’s 2020!! Fireworks are a staple at new year and these beautiful displays wouldn’t be possible without maths πŸŽ†! 2020 is also a leap year – but do you know the maths behind why we have leap years?? And did you know that they aren’t always every 4 years!? πŸ€”

First for the maths of fireworksπŸŽ†πŸŽ‡. Well fireworks work like anything you throw into the air – they follow a curve and eventually start falling back to the ground. It is very important to get the maths right when making fireworks as we wouldn’t want them going off when they have fallen back down! Using maths, you can calculate the height that the firework explodes given the force that propels it into the air (will need to be larger for bigger fireworks). The fuse 🧨 needs to be the correct length so that it burns for just the right amount of time before going off at the fireworks highest point. What we call the β€˜stars’ are the things that light up in each direction to produce amazing patterns in the sky. Since firework shells are usually spherical, the arrangement of the stars inside the shells are propelled out symmetrically to give these lovely displays. πŸŽ†

Why do we have leap years?! Our calendar year is 365 days long; however, the Earth 🌍 actually takes approximately 365.25 days to orbit the Sun β˜€οΈ. Therefore, to keep our calendar πŸ“… in line with how far along the Earth is in its orbit, we need to add an extra 0.25 days to each year. The easiest way to do this is to add one whole day every 4 years….and that is exactly what we do – in our leap years! In fact, the orbit of the Earth can be even more accurately measured as taking approximately 365.2422 days. Therefore, adding an extra quarter day every year is too much! To get us back in line, we do something that not a lot of people know…we skip having some leap years! More specifically, we skip having a leap year if the year:

1. Is a multiple of 100;
2. Is not a multiple of 400.

So the year 2100 for example will not be a leap year!πŸ‘€

We can use maths to check how accurate this method is:

Every 400 years will have 100 (every 4 years) – 3 (not the 100th, 200th and 300th year) = 97 leap years. So we will have 400 – 97 = 303 β€˜normal’ years. Altogether, this will be (303 x 365 days) + (97 x 366 days) = 146,097 days. Every year will therefore have 146,097 / 400 = 365.2425 days. This is very close, but is still not quite right (still a tiny bit too highπŸ™). However, is it so close that we won’t notice the difference for many thousands of years. Scientists will then have to sit down and work out when else we should skip leap years…can you come up with a method that would give us 365.2422 days per year?? πŸ€”πŸ€”

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