Use-the-Gauss-Bonnet-Theorem-to-show-that-the-number-of-holes-in-a-straw-is-1-Then-associate-it-and-show-that-the-Genus-on-the-surface-is-1-

Question Number 224806 by fkwow344 last updated on 05/Oct/25

$$\mathrm{Use}\:\mathrm{the}\:\mathrm{Gauss}\:\mathrm{Bonnet}\:\mathrm{Theorem}\:\mathrm{to}\:\mathrm{show}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{holes}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straw}\:\mathrm{is}\:\mathrm{1}. \\ $$$$\mathrm{Then}\:\mathrm{associate}\:\mathrm{it}\:\mathrm{and}\: \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{Genus}\:\mathrm{on}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{is}\:\mathrm{1}. \\ $$

Answered by MrAjder last updated on 18/Oct/25

$$\int_{{M}} {K}\:{dA}=\mathrm{2}\pi\chi\left({M}\right) \\ $$$$\chi\left({M}\right)=\mathrm{2}−\mathrm{2}{g} \\ $$$${g}=\mathrm{1} \\ $$

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