I knew someone would make this comment. I love HN for this kind of pedantry when it's specific, accurate and doesn't dismiss the entire article for one inaccurate analogy.
The polar diagram shown there is what should replace the ellipse in TFA. It's far more complicated than a simple geometric shape since it has to account for such practicalities as sail inventory.
I didn't know anything about sailing, but your one comment made me search up point of sail and now you've opened my eyes to something that was a mystery to me for all my life -- how sailboats can "course made good" against the wind. Thank you.. this stuff is amazing, and sailing is an incredible science!
A beam reach isn't necessarily the fastest point of sail. It depends on the boat, the efficiency (lift/drag ratio) of the sail, and the efficiency of the centreboard/keel (again, lift/drag ratio), but a reach of some kind is likely to be the fastest - it just won't be exactly perpendicular to the true wind direction. It'll also vary with the wind speed, wave height, weight distribution, etc.