Download 131,000 Historic Maps from the Huge David Rumsey Map Collection
The world has changed dramatically over the past 500 years, albeit not quite as dramatically as how we see the world. That's just what's on display at the David Rumsey Map Collection, whose more than 131,000 historical maps and related images are available to browse (or download) free online.
Today we're sending the first black person & the first woman to the moon.
But I know that Dr. Mae Jemison was the first black woman to travel into space when she served as a mission specialist aboard the Space Shuttle Endeavour in 1992.
https://en.wikipedia.org/wiki/Mae_Jemison
Also, Jemison became the first real-life astronaut to appear on #StarTrek
Here's Jemison as Lt. Palmer in #StarTrekTNG episode Second Chances talking to Nichelle Nichols, Star Trek's Lt. Uhura, outside the set.
#Artemis #Artemis2
We give a near-linear time 4-coloring algorithm for planar graphs, improving on the previous quadratic time algorithm by Robertson et al. from 1996. Such an algorithm cannot be achieved by the known proofs of the Four Color Theorem (4CT). Technically speaking, we show the following significant generalization of the 4CT: every planar triangulation contains linearly many pairwise non-touching reducible configurations or pairwise non-crossing obstructing cycles of length at most 5 (which all allow for making effective 4-coloring reductions). The known proofs of the 4CT only show the existence of a single reducible configuration or obstructing cycle in the above statement. The existence is proved using the discharging method based on combinatorial curvature. It identifies reducible configurations in parts where the local neighborhood has positive combinatorial curvature. Our result significantly strengthens the known proofs of 4CT, showing that we can also find reductions in large ``flat" parts where the curvature is zero, and moreover, we can make reductions almost anywhere in a given planar graph. An interesting aspect of this is that such large flat parts are also found in large triangulations of any fixed surface. From a computational perspective, the old proofs allowed us to apply induction on a problem that is smaller by some additive constant. The inductive step took linear time, resulting in a quadratic total time. With our linear number of reducible configurations or obstructing cycles, we can reduce the problem size by a constant factor. Our inductive step takes $O(n\log n)$ time, yielding a 4-coloring in $O(n\log n)$ total time. In order to efficiently handle a linear number of reducible configurations, we need them to have certain robustness that could also be useful in other applications. All our reducible configurations are what is known as D-reducible.
Coach Pāṇini ®
Niki
Jeff Jarvis
John Siracusa
Lightfighter
Open Culture (Official)
Marin Todorov
Spocko
Zen in Color
Sang-il Oum