In addition to the rich and diversified fauna and flora, the park boasts waterfalls, caves, splendid viewpoints and fascinating ruins.

Soon after walking through the entrance, you pass the Cascatinha Taunay, a waterfall on the Rio Tijuca named after French painter Nicholas Antoine Tournay who bought the estate in 1817, which I had repeatedly seen on tourist propaganda around the city, none of which specified where exactly it was.

Of the multitude of trails to explore, I tackled the 817-metre climb to the Pedra do Conde, a sweaty, muddy pursuit rewarded with views every bit as stunning as Corcovado, setting for Christ the Redeemer.

In addition to hiking, opportunities exist to mountain bike, rock climb, hang glide and even waterfall bathe. While some of those cost, park entry is free, as are the maps available at the visitor centre.

 Average temperatures in the park range from 18 to 26 degrees so expect your shirt to be dripping off you and obviously drinking water is more important than a beanie.

Like the organised tours, I spent five hours hiking in Tijuka. In that time, I passed four other people - an insanely-fit local who uses the trails for his training runs, a couple who looked like locals but said "Good morning" as if educated at Eton, and a like-minded German journalist determined to see the park she had spent the previous fortnight skirting.

Four people. At Corcovado, you can expect as many people in the same space you would normally use to shower.

Apparently, the park receives about three million visitors per year, but, as Corcovado is within its boundaries, that surely accounts for about 2.99 million of those.

From my observations, the rest of the park gets about five per day (three when the Olympics are not present).

As for those bizarre sights back in the city centre, my top three would have to be:

* A Harley-Davidson rider with an unwilling live cat strapped to the front of his bike. In what country would that be considered acceptable?

* An unlit cyclist, clad only in shorts and thongs, pedalling erratically (whilst texting) into oncoming traffic at night with what was most likely his son clinging on behind him.

* A flame juggler. Nothing unusual about that, much the same as you would see entertaining tourists at Circular Quay. Except this flame juggler was doing so in front of traffic at one of Rio's busiest road junctions hoping to get tips from drivers he was simultaneously delaying.

Given such crazy goings-on in the crowded CBD, I'd take the deserted national park any day. And so would the cat on the Harley.