graph LR
    idea_2591f787_fcfb_4647_bcc8_25ab08974ca8["Physics"]
    idea_276874c1_38f1_4f14_a26f_705f8ceb676d["Optimization via Derivative Equating to Zero"]
    idea_46ce42ac_ec93_41ba_a3ec_7636e4fcb911["Euclidean Distance Calculation Using the Pythagorean Theorem in Geometry"]
    idea_8712e4fc_7bcb_4b0a_97a8_c4b332b2bd65["Mathematics in general"]
    idea_a7ab481a_2105_4be2_b5e7_c8396fc49352["Mathematics for nonmathematicians (engineering, social sciences, etc.)"]
    idea_d050c759_7b09_49cb_87f8_7b65781c3dab["Trigonometric Substitution with Sine Functions"]
    idea_fb86545a_cb87_419a_aaf5_d001203f779f["Fermat's Principle of Least Time and the Derivation of Snell's Law"]
    idea_a7ab481a_2105_4be2_b5e7_c8396fc49352 --> idea_fb86545a_cb87_419a_aaf5_d001203f779f
    idea_46ce42ac_ec93_41ba_a3ec_7636e4fcb911 --> idea_fb86545a_cb87_419a_aaf5_d001203f779f
    idea_d050c759_7b09_49cb_87f8_7b65781c3dab --> idea_fb86545a_cb87_419a_aaf5_d001203f779f
    idea_8712e4fc_7bcb_4b0a_97a8_c4b332b2bd65 --> idea_fb86545a_cb87_419a_aaf5_d001203f779f
    idea_276874c1_38f1_4f14_a26f_705f8ceb676d --> idea_fb86545a_cb87_419a_aaf5_d001203f779f
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    style idea_2591f787_fcfb_4647_bcc8_25ab08974ca8 fill:#7f1d1d,stroke:#450a0a,color:#fca5a5
    style idea_a7ab481a_2105_4be2_b5e7_c8396fc49352 fill:#7f1d1d,stroke:#450a0a,color:#fca5a5
    style idea_fb86545a_cb87_419a_aaf5_d001203f779f fill:#e5e7eb,stroke:#9ca3af,color:#374151
    style idea_8712e4fc_7bcb_4b0a_97a8_c4b332b2bd65 fill:#7f1d1d,stroke:#450a0a,color:#fca5a5
    style idea_46ce42ac_ec93_41ba_a3ec_7636e4fcb911 fill:#fef3c7,stroke:#f59e0b,color:#92400e
    style idea_d050c759_7b09_49cb_87f8_7b65781c3dab fill:#fef3c7,stroke:#f59e0b,color:#92400e