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Concerning Deane Yang's 4th point, permit me to cite the earlier MathOverflow question, "$C^1$ isometric embedding of flat torus into $\mathbb{R}^3$," which displays (and links to¹) some amazing images from the Hévéa² project's illustration of the Nash-Kuiper $C^1$ embedding theorem applied to the flat torus:

Concerning Deane Yang's 4th point, permit me to cite the earlier MathOverflow question, "$C^1$ isometric embedding of flat torus into $\mathbb{R}^3$," which displays (and links to¹) some amazing images from the Hévéa² project's illustration of the Nash-Kuiper $C^1$ embedding theorem applied to the flat torus:

Concerning Deane Yang's 4th point, permit me to cite the earlier MathOverflow question, "$C^1$ isometric embedding of flat torus into $\mathbb{R}^3$," which displays (and links to¹) some amazing images from the Hévéa² project's illustration of the Nash-Kuiper $C^1$ embedding theorem applied to the flat torus:

Concerning Deane Yang's 4th point, permit me to cite the earlier MathOverflow question, "$C^1$ isometric embedding of flat torus into $\mathbb{R}^3$," which displays (and links to¹) some amazing images from the Hévéa² project's illustration of the Nash-Kuiper $C^1$ embedding theorem applied to the flat torus:

Concerning Deane Yang's 4th point, permit me to cite the earlier MathOverflow question, "$C^1$ isometric embedding of flat torus into $\mathbb{R}^3$," which displays (and links to¹) some amazing images from the Hévéa project²:

Concerning Deane Yang's 4th point, permit me to cite the earlier MathOverflow question, "$C^1$ isometric embedding of flat torus into $\mathbb{R}^3$," which displays (and links to¹) some amazing images from the Hévéa² project's illustration of the Nash-Kuiper $C^1$ embedding theorem applied to the flat torus: