graph LR
    idea_677b9265_5b4d_44a8_b0ac_e9cec2683259["Completing the Square for Gaussian Exponents"]
    idea_818ce6b4_5455_4536_abae_f731a068a004["Deriving Pi in the Gaussian Distribution from Radial Symmetry and Independence"]
    idea_85e11bbc_85e6_4595_be2d_ad642ad43399["Integration by Substitution in Real Analysis"]
    idea_9efac48c_5a5d_4ac7_9a7c_bdc3bf62c85c["Convolution Stability: Why the Sum of Two Gaussians Is a Gaussian"]
    idea_ada7a087_245e_4cc0_90a8_7046909da8f3["Rotational Symmetry in Two-Dimensional Functions"]
    idea_b2d41e2d_0522_4bbf_9200_dd463023c2af["Cylindrical Coordinates Transformation"]
    idea_b6c392d5_8da3_4507_8cb6_29881e84e513["Convolution Operation for Summing Independent Random Variables"]
    idea_fe901134_4efb_4ed4_b82b_e8dfbf1f2e88["Volume of Revolution and Pappus's Theorem"]
    idea_b2d41e2d_0522_4bbf_9200_dd463023c2af --> idea_818ce6b4_5455_4536_abae_f731a068a004
    idea_ada7a087_245e_4cc0_90a8_7046909da8f3 --> idea_9efac48c_5a5d_4ac7_9a7c_bdc3bf62c85c
    idea_b6c392d5_8da3_4507_8cb6_29881e84e513 --> idea_9efac48c_5a5d_4ac7_9a7c_bdc3bf62c85c
    idea_677b9265_5b4d_44a8_b0ac_e9cec2683259 --> idea_9efac48c_5a5d_4ac7_9a7c_bdc3bf62c85c
    idea_85e11bbc_85e6_4595_be2d_ad642ad43399 --> idea_818ce6b4_5455_4536_abae_f731a068a004
    idea_fe901134_4efb_4ed4_b82b_e8dfbf1f2e88 --> idea_818ce6b4_5455_4536_abae_f731a068a004
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    style idea_818ce6b4_5455_4536_abae_f731a068a004 fill:#e5e7eb,stroke:#9ca3af,color:#374151
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