## Calculer la conductivité thermique de mon appartement

Je vis dans un appartement montréalais typique : mal isolé et chauffé avec des plinthes électriques. Puisque l’électricité est l’unique source d’énergie utilisée pour chauffer  l’appartement et qu’Hydro-Québec fournit sur son site web une mesure de la puissance moyenne consommée pour chaque heure de la journée, j’ai pensé que je pourrais essayer d’estimer la conductivité thermique absolue de mon appartement.

## Measuring my apartment’s thermal conductivity

I live in a typical Montréal apartment : poorly  insulated and heated with electric baseboards. Since electricity is the only source of heat in my apartment and Hydro-Québec, Québec’s electricity provider, provides an hourly measurement of our electricity consumption, I thought I could try to estimate the absolute thermal conductivity of my apartment.

## Analytical equirectangular projection of great circles

We previously analyzed the equirectangular projection of great circles using sampling and simulations. This was done mostly to visualize the shape of the curve and understand its behavior. This time, let’s try to find an analytical solution to describe the curve of a great circle in an equirectangular map.

## Equirectangular projection of a great circle

A few years ago, I was working with equirectangular projections of spherical data (mostly spherical panoramas and spherical depth maps) for a 3D reconstruction research project. For a reason I can’t remember, I started wondering what a great circle would look like in an equirectangular projection. A great circle is the intersection between a plane and a sphere if the plane intersects the center of the sphere.

To get a quick answer, I drew a rough sketch of a great circle on a sphere. On the sphere, I marked the meridians and parallels at 45° intervals. Then, I sampled the great circle where it intersects with the meridians and parallels and mapped those points on an equirectangular map. Finally, I drew a curve between the sampled points to get the results shown in figure 1.

## Montreal gas prices

Montrealers know how the gas prices in the region like to jump around. I have decided to analyze this price volatility. In particular, I asked myself if it is possible to predict when the prices will be lower by analyzing the historical prices .

For the impatient, the answer is : yes! During the year ending on May 25 2018, the sudden price increases didn’t happen at purely random moments. If you had filled up your car only on Monday during this period, you would have saved up to 3% on your gas bill.

## Prix de l’essence à Montréal

Les résidents de la région de Montréal savent que le prix de l’essence aime jouer au yoyo dans la région. J’ai décidé d’analyser cette forte volatilité des prix. Plus particulièrement, je me suis demandé si en analysant l’historique des prix il est possible de prévoir quand les prix seront plus bas pour économiser.

Pour les impatients, la réponse est : oui! Lors de l’année se terminant le 25 mai 2018, les hausses soudaines de prix n’ont pas eu lieu à des moments purement aléatoires. Si vous aviez fait le plein de votre automobile uniquement les lundis durant cette période, vous auriez pu économiser jusqu’à 3% sur votre facture d’essence.