The scaling constant observed in these transformations—ranging from 1 in 2D to 6 in 4D—serves as a geometric scaling factor determined by the number of valid index permutations in a given dimension. While 2D operations relate to simple vector projections and 3D contractions underpin the standard BAC-CAB vector identity, higher dimensions like 4D involve hyper-volume scaling determined by the $(n-1)!$ factorial growth. This progression highlights how antisymmetric tensor products consistently collapse into symmetric, manageable scales across different spatial complexities.
block-beta
columns 5
CC["Criss-Cross"]:5
%% Condensed Notes
CN["Condensed Notes"]:5
RF["Relevant File"]:5
NV["Narrated Video"]:4 VO["Voice-over"]
PA("Plotting & Analysis")AA("Animation & Analysis")KT("Summary & Interpretation") ID("Illustration & Demo") PO("Polyptych")
%% Proof and Derivation
PD["Proof and Derivation"]:5
AF("Derivation Sheet"):5
NV2["Narrated Video"]:4 VO2["Voice-over"]
PA2("Plotting & Analysis")AA2("Animation & Analysis")KT2("Summary & Interpretation") ID2("Illustration & Demo") PO2("Polyptych")
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%% %% Condensed Notes
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class RF color_2
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class PA color_3
class AA color_3
class KT color_3
class ID color_3
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class VO color_4
class PO color_4
%% Proof and Derivation
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class PD color_5
class AF color_5
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class NV2 color_6
class PA2 color_6
class AA2 color_6
class KT2 color_6
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class VO2 color_7
class PO2 color_7
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