Science Writing
Science
Enter mathematics through a question, then return from mathematics to the way we understand the world. This collection gathers science articles made to be read and explored.
Science · Game Theory
Honor of Kings · Solo-Lane Invasion at 1:30
After clearing the first mid wave, the mid laner and support immediately rotate towards the Overlord side and invade the enemy jungle beside the solo lane. The solo laner clears the wave and joins them, bringing the first team fight forward to minutes 1 to 2.
Use the real S43 battlefield map to explore two branches. When ahead, repeatedly pressure red and blue buffs and force a fight around the Tyrant. When behind, stop initiating interactions and look for a defensive counterattack after minute fourteen.
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Science · Game Theory
Honor of Kings · Three-Factor Game-Theory Simulator
Place the gold gap, composition strength and team-fight resolution inside one simulation model to observe the leading side's decisive window, the trailing side's period of avoidance and the moment when a team behind should take a fight.
Adjust lane pressure, kill difference, composition curve and execution noise to see how an economic advantage is diluted over time, and when to fight or wait.
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Science · Mathematics
The Kakeya Problem · Three Dimensions: Rotating a Needle in Space
Make a unit line segment point in every direction in three-dimensional space, and interactively observe how four Kakeya constructions make the occupied volume approach zero.
Rotate, zoom and switch constructions to see how complete directional coverage and arbitrarily small volume can occur together.
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Science · Mathematics
The Kakeya Problem · In the Plane: How Much Space Does a Turning Needle Need?
Rotate a unit-length needle continuously through 180 degrees in the plane, comparing five ways to turn it around: about one endpoint, about its midpoint, inside a triangle, inside a deltoid and through a Perron tree.
Switch constructions and adjust the depth of the Perron tree to see the swept area shrink from a semicircular disc towards an arbitrarily small value.
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Science · Mathematics and Philosophy
The Yoneda Lemma · Everything Is Relation
To know a thing is to know the totality of its relations with everything else. Enter category theory through an interactive philosophical note.
Follow morphisms, functors and natural transformations to see how an object is characterised by its relations with the whole world.
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