Math with Bad DrawingsCartoon Archive

Math Fashion Tips

May 25, 2025

Fashion commentary on equivalent ways of writing the same math: arcsin vs. sin⁻¹, two forms of the derivative, two forms of Euler's identity, factored vs. expanded, two phis, simplified vs. unsimplified radicals, two variance formulas.

Fashion commentary on equivalent ways of writing the same math: arcsin vs. sin⁻¹, two forms of the derivative, two forms of Euler's identity, factored vs. expanded, two phis, simplified vs. unsimplified radicals, two variance formulas. (panel 1 of 7)
Panel 1Download panel
Fashion commentary on equivalent ways of writing the same math: arcsin vs. sin⁻¹, two forms of the derivative, two forms of Euler's identity, factored vs. expanded, two phis, simplified vs. unsimplified radicals, two variance formulas. (panel 2 of 7)
Panel 2Download panel
Fashion commentary on equivalent ways of writing the same math: arcsin vs. sin⁻¹, two forms of the derivative, two forms of Euler's identity, factored vs. expanded, two phis, simplified vs. unsimplified radicals, two variance formulas. (panel 3 of 7)
Panel 3Download panel
Fashion commentary on equivalent ways of writing the same math: arcsin vs. sin⁻¹, two forms of the derivative, two forms of Euler's identity, factored vs. expanded, two phis, simplified vs. unsimplified radicals, two variance formulas. (panel 4 of 7)
Panel 4Download panel
Fashion commentary on equivalent ways of writing the same math: arcsin vs. sin⁻¹, two forms of the derivative, two forms of Euler's identity, factored vs. expanded, two phis, simplified vs. unsimplified radicals, two variance formulas. (panel 5 of 7)
Panel 5Download panel
Fashion commentary on equivalent ways of writing the same math: arcsin vs. sin⁻¹, two forms of the derivative, two forms of Euler's identity, factored vs. expanded, two phis, simplified vs. unsimplified radicals, two variance formulas. (panel 6 of 7)
Panel 6Download panel
Fashion commentary on equivalent ways of writing the same math: arcsin vs. sin⁻¹, two forms of the derivative, two forms of Euler's identity, factored vs. expanded, two phis, simplified vs. unsimplified radicals, two variance formulas. (panel 7 of 7)
Panel 7Download panel

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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.

Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2025-05-25-math-fashion-tips/ (CC BY-NC 4.0)
Transcript

[Pairs of notations, one styled blue (unfashionable), one red (fashionable)]

[1] sin⁻¹(x): "sterile, soulless, mass-produced" vs. arcsin(x): "STEAMPUNK, HANDMADE, CONVERSATION STARTER"

[2] lim_{h→0} (f(x+h) − f(x))/h: "persnickety, overly fussy, like a coat with teeny tiny buttons" vs. lim_{x→a} (f(x) − f(a))/(x − a): "breezy, natural, like a breathable fabric"

[3] e^(πi) = −1: "simple, provocative, 'little black dress'" vs. e^(πi) + 1 = 0: "overegging the pudding, too clever by half"

[4] x⁴ − 1: "coy, flirtatious, a hint of mystery" vs. (x − 1)(x + 1)(x − i)(x + i): "messy, overshare, like explaining a dream to someone"

[5] ϕ: "SCOLDING, UPTIGHT, SCHOOLMARMISH" vs. φ: "casual, elegant, 'the cool teacher'"

[6] 7√2 + 3√2 = 10√2: "obvious, uninspired, corporate" vs. √98 + √18 = √200: "buzzy, eyebrow-raising, alluringly suspicious"

[7] (1/n)Σ(xᵢ − x̄)²: "fragile, a museum piece, not as comfy as it looks" vs. E(X²) − (E(X))²: "flexible, durable, everyday wear"

Topics
Math Culture › NotationTrigonometry › Inverse Trig FunctionsCalculus › Derivatives › Limit DefinitionAlgebra › Complex Numbers › Euler's IdentityAlgebra › FactoringNumber & Arithmetic › Square Roots › Simplifying RadicalsStatistics › VarianceAlgebra › Equivalent Expressions
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