German engineers knew about the benefits of sloped armor when they designed the Tiger 1. They decided against it because:

• they trusted their "superior" steel quality (that's a topic on its own)

• the 100mm of frontal armor were more than enough to stop enemy rounds at the time even at a 90° angle. The Tiger crews received extensive training to position their tank in a perfect angle to the enemy so that the armor thickness would be optimised. Here is a page in the Tiger 1 handbook, the red dots on the clock represent the optimal location of an enemy tank: http://i.imgur.com/J4d0y.jpg

Here is a more detailed graph from the handbook specifically for enemy T-34. Red means the Tiger is safe, green means the Tiger is in danger of being penetrated: http://www.matrixgames.com/forums/upfiles/21246/E29EB6B90C044610843ED409CBB1BB70.jpg

If you think the colors red and green are placed quite counter intuitively: it was done so that the danger zone resembled a cloverleaf. Crews were supposed to always keep the enemy out of their cloverleaf. The Tiger can actually penetrate the T-34s armor in all of the red area (smaller red circle for T-34 front and bigger red circle for sides and back).

• sloped armor limits the gun size. This is one of the major points against sloped armor. The maximum width of a tank is pretty much fixed because it can't be wider than the railway system allows. So assuming you place the sides of the tank at that maximum width and slope the armor plates inwards. You are now reducing the roof width of the tank. Why is that important? Because the turret ring has to fit between the sides, essentially onto the roof. So by sloping your sides you are reducing your turret ring diameter. And the turret ring size is the greatest factor that determines turret and therefore gun size. You want a big gun, you need a big turret, you need a big turret ring diameter, you need a wide roof. The turret ring diameter actually is what prevented the T-34 from being upgunned even further after the 85mm gun was installed. There were are few more tests with bigger guns, but it was a nightmare for the loader.

• sloped armor limits internal space. German tanks had a huge transmission in the front as well as a big radio unit. There was not much space to move this equipment back to allow for a sloped front. Also the space above the tracks (sponsons) were used to store ammunition in. The number of rounds the Tiger could carry would have been severely reduced by sloping the sides.

• sloped armor changes the center of gravity. There were tests done with sloped armor on the Panzer IV that revealed that a sloped frontal plate would move the center of gravity even further to the front. THe same issue could be expected for the Tiger.

In the end the engineers thought that their approach was good enough and that the disadvantages of sloped armor outweight the advantages.

which would have resulted in a light and therefore more mobile tank (while also using less steel--presumably a valuable resource even at that time).

The Tiger 1 was designed as a breakthrough tank. For mobility the German Amy used the Pz IV and later the Pz V Panther tank. Also at the time the Tiger was designed German economy didn't suffer under shortages as it would later in the war.

edit: sorry for not providing any sources apart from the photos. I just can't remember where exactly I read all that. I think you can find most of the crew handbook stuff in the Tiger-Fibel. Regarding the decisions against sloped armor you would have to use the appropriate book from Jentz & Doyle or Spielberger.

When examining the design of the Tiger 1 understand that it was over engineered to completely outclass other tanks of that era. I'll breakdown the support of my answer into three categories, armor, guns, and tactics.

Frontal hull armor of the Tiger 1 tank was roughly 100mm and the frontal turret armor was an absurd 120mm. The T-34 frontal armor was roughly 60mm thick, even applying the rule of cosines for its slanted means that a shell fired directly at its front would encounter armor 70mm thick.

The 88 mm KwK 36 L/56 gun (German) and the F-34 76.2 mm (Russian) weapons were both some of the best tank guns during ww2. The F-34 was capable of penetrating 92 mm armor at arrange of 500m. It’s successor the 85mm ZiS gun (introduced in 1942 post Operation Barborosa), could penetrate Tiger 1 front armor at a range of 200 to 500m. The Tiger 1 88mm gun could penetrate the front armor of a T-34 at a range of 800 -1400m.

This means that the T-34 was capable of penetrating a Tiger tank but only at its flank, and even then they fired at a much slower rate. German commanders reported that T-34’s were so slow at finding and engaging targets that their tanks could fire 3 rounds for every 1 fired by a T-34.

So in answer, the German’s Panzer was a balanced mobile tank, but the German commanders wanted a mobile fortress. Sloping the armor gives you a marginal gain when comparing tanks of similar guns and armor. The Germans didn’t need sloped armor because their tank outclassed their opponents so significantly in armor and guns. I would go as far to say that if a greater number of T-34’s were flanking stationary Tigers, it would be a pretty even fight.

There are several reasons for that. First the Tiger I was unmatched on the battlefield when it was released so the engineers apparently didnt think it was necessary to use sloped armor. Secondly the armor of the Tiger I was designed so it would destroy an enemy grenade instead of deflecting it, basically the armour consisted of 3 armor plates, so you had a better chance at frontal assaults against bunkers or something similar.

Edit: besides that, sloped armor plates would have made the Tiger I even more heavier than it already was