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Geometry MM: Pythagorean Theorem 3 (Prison Complex Main Floor - North Wing Lever Room): NWN 0114

Echoes of experiencing Shar persist as she remains in deep contemplation of its spellbinding beauty, its unimaginable enormity and its emotional anguish. During this time the ceaseless noise of rioting prisoners increasingly intrudes on her preoccupation and slowly loosens Shar's hold on her, until the violent crashing of glass severs her fixation. Annoyed by the intervention, Zanzi picks up her crossbow, instructs Tomi to follow her and continues her prison quest with an even greater strength of purpose. From the main entrance office she enters the north wing lever room, casting Invisibility and entering stealth mode before doing so. Once inside she sees four prisoners and immediately sets to the process that will end their lives. Her Curse Song, Bard Song, spell casting and ranged weaponry skills make short work of the task and within 30 seconds all four men are dead. She pulls a lever that opens all the doors to the north wing prison cells then says to Tomi, "Saves you having to pick the locks. Let's get out of here."
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Zanzi's skill with her crossbow increases every time she uses the weapon and by quickly calculating the distance between herself and her adversaries by digitally constructing an imaginary right triangle and calculating the hypotenuse using the Pythagorean theorem, she is able focus ever more precisely on the vulnerabilities of her target. Of the four bolts she fired during this combat for instance, one hits less than an inch below an eye, another about an inch left of a mouth, another nicks the superior vena cava of a heart and the last pierces the right atrium of another heart.
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By placing herself at the centre of a digitally constructed imaginary circle, Zanzi is able to calculate using the equation for a circle whether her Bard and Curse Songs will affect her allies or enemies, neither of whom must be farther than 30 feet from her for her songs to phase.
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It soon becomes clear to Zanzi that something has managed to comprise the security subsystems that protect her body constructs from infiltration. She comes to this realisation after running a routine diagnostic program that identified two foreign polygons located in her amygdalae. The diagnostic digitally constructs a unit circle that circumscribes each polygon in her body. When it circumscribed a unit circle around the 30-60-90 and 45-45-90 triangles implanted by the entities from the positive and negative energy planes, it encountered anomalous values for the coordinates of these polygons (nothing in her amygdalae should provide coordinates for these types of triangles) . The diagnostic then relayed this information to Zanzi's master parallelogram which then made her aware of these alien triangles. Zanzi instructs the diagnostic program to eradicate the triangles but the energies from which they are constructed are also alien and the program cannot even begin to neutralise them. The fact she cannot rid herself of these polygonal violations and the fact they are located deep within her brain is greatly unsettling to Zanzi, especially as she is unaware how or why they were generated, or by whom, although she strongly suspects - no, she knows - the Shar visitation is non-coincidental.