The Death Triangle is one dangerous, incorrect way to build anchors for rock climbing or rappelling. It's instructive to talk about, because it represents an attempt to make the anchor safe, but actually has the opposite effect.
(Before I go any further, a disclaimer: this node only describes one particular, common error. Reading E2 does not teach you how to build safe anchors nor how to climb rocks without dying.)
The name "American Death Triangle" was coined by Canadian and European climbers, who first saw such anchors on visits to the United States. American climbers at the time were mostly self-taught, while the visitors tended to have formal training which helped them spot the Americans' mistakes.
The mistake here arises because any safe anchor is attached to at least two solid things, like bolts or trees or immovable rocks. Call those "hardpoints", and you need at least two because any good anchor is redundant. If one of the attachment points fails for any reason, the anchor must still remain in place to prevent you from plunging to your death.
You, the climber, must be connected to both hardpoints. The best way to do this is to connect the hardpoints together first, and then attach your rope or belayer to the "power point" where they are joined. Most simply you would do this by using two nylon slings. You attach one sling to point A, another one to point B, and then clip them together with a carabiner, as in this simplified (and poorly-rendered) example:
* is a bolt in the rock face
- is a strand of a nylon sling
@ is a carabiner at the power point
\\ // This could be a decent anchor.
Here comes the dangerous bit. If you're a newbie, and all you know is that your anchor needs two points of support, you may try to do this with one nylon sling. You might clip that sling to both anchor carabiners, and clip your rope to a point in the middle. That construct is the Death Triangle, and it looks like this:
\ / This is not safe.
The problems with the Death Triangle are threefold. First, it's fragile. The whole thing depends on that one sling, a single point of failure. If the sling breaks or comes untied, there will be nothing else holding you up, and you will plunge to your death.
Second, it allows extension. If one of the bolts fails, there's nothing else to hold that sling in a big open triangle. Your weight pulling on the power point will immediately draw the slack out of the loop. When it snaps taut, that sudden jerk will put a momentary tremendous force on the second bolt. Since that force is so great, that remaining bolt is likely to break also, which will leave you again unanchored and plunging to your death.
Third, the really counterintuitive part: the geometry here multiplies the force on the hardpoints. As the rope pulls downward, it's obvious that the sling exerts downward force on the bolts. But less obviously, the tightening of the sling also pulls the bolts toward each other. Depending on the angle between the bolts and the power point, this inward force can be more than three times as great as the downward force.
In a worst-case scenario, a caught lead fall can generate a downward force approaching 20 kilonewtons at the power point. When passed through a tightening triangle with a 150° angle, that could translate into 76 kilonewtons on each bolt. That much force can shear bolts and bust anchors, and if that happens, a plunge to your death will immediately follow.
So don't do that.