My solution to the model kerb slide activity

I could have modelled this just using piece-wise functions with restricted domains. When it was loaded into Geogebra though it was clear that the bottom left section was doing more than just being horizontal. There is a definite negative (but increasing towards zero) gradient… sounds a bit like an exponential decay function to me.

Dan's solution from Geogebra.
I used a piece-wise and an exponential decay graph for my model. What did you get?

My Geogebra model – feel free to use it and modify it to see if you can make it a better fit to ‘the data’, AKA the wall.

Pro-Tip: The thicker the line, the better the fit. This is a joke.

Model kerb slide?

How could you use what you know about functions to model this image? Credit: Guillermo Suarez on Unsplash

Pinning it down, reluctantly

  • use any functions to model the wall that the guy is skating along above.
  • Try to be specific about what domains you want your functions to occupy
  • be as creative as you wish, or as lame
  • bon voyage!

Links

Who is our nearest planetary neighbour?


Our fellow wanderers, Venus, Mars & Mercury. But who is the closest?

A loyal listener to the BBC’s excellent “More or Less” podcast asked the other day about which planet is our nearest neighbour. He had heard on TV that it was Mars, but he himself thought it was Venus, so he asked them to investigate. 50 years of data were duly collected and dispatched, to an illustrious Professor, who revealed the answer on the show (link below!), so well done More or Less!

But hang on a moment. I am pretty sure that regardless of your existing astronomical knowledge, you will be able to figure this answer out for yourself, with just 50 seconds of data if you read on… What’s more, for the vast majority of human history nobody at all could have answered this question, and now we can do it on our ‘phones’. Simply wow!

HINT: The planets are named after the Greek word “planetes”, which means “wanderers”. Bear this in mind as you think about this problem.

So which planet is our nearest neighbour?

Mars’ Mariner Valleys – thanks to NASA for the gorgeous photo

Isn’t it Mars? Humans have been sending rovers to survey the place, and do plan on sending a manned, one-way mission at some stage. But it will take some 300 days to get there, and that is if you launch when our two planets are at their closest. Mars was also described as “planet Earth’s closest neighbour” on the BBC’s ‘Sky at Night’ program the other day too. Hmmmm.

Could it be Venus? I am pretty sure I have been told that Venus is the closest planet, and that is what my instinctive answer would be. There were loads of stories about aliens on Venus coming to invade Earth back when sci-fi was first starting to become popular many decades ago, so it would make sense as a choice.

Venus. This image was created using combined data from the Magellan, Pioneer and Venera data. Three separate missions were needed to create this image!

Why not Mercury? (The planet, rather than the metal AKA quicksilver) Named after the winged messenger of the gods from Greek mythology, and closest planet to the Sun, it sounds fast and it is hot enough to melt lead at its equator. Surely too hot to be the closest neighbour of our beautiful blue-green Mother Earth?

The classic school poster of the Solar System. Pretty planets all in a row!
Does this beautifully neat image help us answer the solve the problem? Afraid not! See this article.

If you are looking for the solution, the picture above does not help, at least not much. And sure I could just tell you, but wouldn’t you rather figure it out for yourself? If you just visit this amazing model of the Solar System provided by Solar Scope and play around for a few minutes you will be able to solve this mystery for yourself – I promise! Zoom in until you can see all the contenders, speed up time a few notches, and watch carefully… You may be surprised!

If you don’t have time to figure it out for yourself, feel free to watch this short video where I reveal the truth!
If you are really short of time, scroll down to see the answer! I recommend that you also listen to the recent BBC More or Less program to hear a great discussion of this, but please make sure to also check out the amazing model from Solar Scope. It’s one of the highlights of the internet and it makes the problem super easy to solve.

Go play with this model and find out the answer to this riddle, and so much more!

Links to models – go play!

The solution…..⅄ɹ∩ƆɹƎW!

Earth’s nearest planetary neighbour, at least for the majority of the time, is Mercury. Venus spends less time than Mercury as our nearest but actually approaches closer than any other planet, while Mars is occasionally the closest, and has the most similar orbital velocity.

Thanks for reading!