In SM64 this covering space structure is used by giving Mario extremely high velocity \(v\) (a tangent vector at Marios position in \(P\)) through a different glitch called “backwards longjump”. The exponential map is then used to move Mario along the geodesic \(\exp_v(t)\) for \(t \in \mathbb{R}\). But due to hardware limitations, only discrete steps \(t_1, \dots, t_k\) for some \(k \in \mathbb{N}\) of this geodesic are actually calculated for collision detection. More on how this is related to the exponential map of Lie groups can be found in my previous post. Throughout this post, I will assume the Lie group of SM64 to have its unit at the position \(p\).
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The iPad Air still comes in 11-inch and 13-inch versions that start at $599 and $799, respectively; the only disappointment is that these entry-level models still come with 128GB of storage. A 256GB storage upgrade will run you $100, and 512GB (+$300) and 1TB (+$500) versions are also available. Preorders go live on March 4, and the tablet will be available on March 11.