Leap Years: we can do better

in Coincidence by

2016 is a leap year because it is a multiple of 4 (and not a multiple of 100). The Gregorian Calendar system of leap years gives an average tropical year of 365.2425 days compared to the current true value of 365.2421891, but I think we can do better.

Yes, at the 1:20-ish point it should be “365.2421891 days” as is on the screen, not the “365.2521891 years” I say. Sorry, it’s been a busy week and I recored and edited the video a bit too quickly to spot Past Matt’s mistakes.

Read Adam Goucher’s article here:

Music by Howard Carter
Design by Simon Wright

MATT PARKER: Stand-up Mathematician
Nerdy maths toys:


  1. 31 Days in 128 ?? What happens to each year before 128 years… drifted long ago.
    If its no matter then I suggest even better
    > 365 days of year with 2421891 days added after every 10^7 years. problem solved!

  2. Or we could use fractions of certain events to determine time; use measurements of the Earth's tilt relative to its plane of orbit to determine the length of a year, and fractions of that to determine months. Use the Earth's rotation relative to its orbital path to determine the lengths of days, and fractions of that for hours and minutes. I'd leave seconds alone as a constant for scientific measurements, so that they no longer have to measure up with the minutes. Either that, or use a time unit derived from the time it takes for light to travel a certain distance; a universal constant. I don't think that anybody particularly cares that the ends and beginnings of years and months line up with the exact beginnings and ends of particular days, anyway; this opens up the possibility of, say, having a new year happen across the world at the same time.

  3. so my big question here is.. for those of us (like me) that were born on leap day (in my case, 02/29/1988), when will my real birthday fall under all of these systems?

  4. Or write it in Hexadecimal. If the last digit is a 0, a 4, or an 8 its a leap year unless the last 2 digits are 80 or 00 (80 is 128)

  5. hooray for the jewish calendar, which has leap MONTHS because it's a lunar-based calendar. Not only that, but the name of that extra month is extremely creative…

  6. if we really cared, we could just accelerate or slow down the earth with turreted rockets at the poles or something…

  7. Did Matt watch Tony Padilla's conclusion world will end after 8600 years du to our population exponential growth? Hence that idea the calendar projects are poinless… 🙂

  8. In the distant future… Mathematicians are wondering if the year 11825792 is a leap year. By the Julian Calendar, it is as it is a multiple of 4. By the Parker Calender… they cant decide, until they write it in binary to: 101101000111001010000000 and realise it shouldn't be a leap year! until they realise it has deviated by 129 days at this point, and they need to redesign another calender.

  9. Hi, did you start counting years from year 1 or 0 ? Can you give as a mathematical pattern which you use to calculate a year drift?

  10. In Russia, the Julian calendar continued to be used, which is why the October revolution actually happened in November (they adopted the Gregorian calendar afterwards)

  11. The best solution is to have two clocks for humanity:

    1 – a master clock that ticks steadily on, for example unix time but without the leap seconds.

    2 – a clock synchronised to the orbit of earth around the sun via negative feedback.

    For god sakes, the solar system itself if you stand/sit/hover above the solar system's plane, and look down at the earth going around the sun, it makes a giant space clock. And this is the clock we are trying to approximate with out calendar and all the leap year bullshit. God GAVE us a clock, and we are too stupid to use it.

    And for the master clock, you can just draw a tree graph for the various levels of the hierarchies. All the internet stock market synchronization business, etc, is much easier handled with this guy than with a clock that perpetually fails to be on time (ie, the one clock we are trying to all use today). It's so stupid that we even have Daylight Savings Time in some places and not others, just to make the clock that much more complicated.

    Wake up people. Make 2 clocks. A master clock, and a synchronised clock. There. Problem solved. Where's my cheque?

  12. So, with the Earth days slowing by 1.xx milliseconds every 100 years, by the end of the 53.5 trillion years (of the fixed Julian calendar), the calendar would've drifted…

    >170 years!!!

  13. We're kidding ourselves trying to add days and years together, they aren't related in a meaningful way. We could write the time as a complex number denoting the angle of rotation we are through each cycle. For example pi/2 of a year + pi of a day is about may 1st, mid day. Months are more related to years than days so we could write those as multiples of pi/6 year if we wanted to be nostalgic about our old system. Of course very few people would be comfortable with such a system, nevertheless I'd love to see a clock that represents time as angular fractions of only real measurements such as galactic year -> solar year -> earth spin -> earth tilt cycle

  14. i think leap years are bad. Its more exciting that seasons are swaping
    I would make year 362 yeaers so seasons constantly swap

  15. I think he means put back a leap day in a year that is a multiple of 625,024 (itself multiple of 128), not take it out. But that is truly a tiny quibble. The 128-year calendar is a great idea. But someone has pointed out that the same net result (a calendar year of 365.2421875 days) can be achieved by modifying our Gregorian calendar to omit the leap day every 3200 years (every 8th 400-year cycle).

  16. An interesting argument is that a little more than 3500 years ago the year seemed to be exactly 360 days and in a VERY short time increased to 365+. There is written Biblical evidence to this change, but there is also evidence that other civilizations also observed this, as well. The Mayan and Aztec calendars, for example, based on actual measured observations of the sun's shadow at the summer and winter solstices was exactly 360 days. The ancient Babylonian and even older Sumerian calendars were 360 days long. The Bible recounts a story in Isiah that tells that the shadow on the sun dial moved backwards a total of 10 degrees. About 2200 years ago the Egyptians realize something had gone wrong with their calendar and apparently kept the accepted 360 day calendar, but added 5 days not associated to any particular month to the end of each year.

    The only thing that could have this effect (as far as I know) is either human's perception of time drastically changed in a day or (more probable) the Earth was somehow bumped into a higher orbit, not just a translation but an increase of the mean distance from the sun, which has the overall effect of slowing it down.

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