Geoff Krall, PhD

@geoffkrall.bsky.social

460 Followers 218 Following

Math and the like. Asst Professor at Colorado State University. Author of 'Necessary Conditions'.

Chyron that says "If you took 22-inch Dachshunds and laid them notes to tail you'd need 728 million dogs to cover the distance" in reference to Artimis II's journey around the moon,
An orange feather within two script brackets. From the videogame Celeste
Three venn diagrams 1) two circles overlapping 2) circle (pck) within a larger circle (ck) 3) same circle 4) question mark
Excerpt from Paul Lockhart's "A Mathematicians Lament" Teaching is not about information. It’s about having an honest intellectual relationship with your students. It requires no method, no tools, and no training. Just the ability to be real. And if you can’t be real, then you have no right to inflict yourself upon innocent children. In particular, you can’t teach teaching. Schools of education are a complete crock. Oh, you can take classes in early childhood development and whatnot, and you can be trained to use a blackboard “effectively” and to prepare an organized “lesson plan” (which, by the way, insures that your lesson will be planned, and therefore false), but you will never be a real teacher if you are unwilling to be a real person. Teaching means openness and honesty, an ability to share excitement, and a love of learning. Without these, all the education degrees in the world won’t help you, and with them they are completely unnecessary. It’s perfectly simple. Students are not aliens. They respond to beauty and pattern, and are naturally curious like anyone else. Just talk to them! And more importantly, listen to them!
"A graph of a smooth blue curve with two local minima and one local maximum. Six vertical dashed lines labeled x1 through x6 are shown beneath the curve along the x-axis. The curve starts high to the left and decreases to a minimum just after x1. The function then increases higher through x2 and achieves a local maximum at x3. The function is decreasing when it passes through the y-axis and decreasing more steeply at x4. The function achives a deeper minimum at x5 before rising steeply through x6.
Screenshot of the royal tenenbaums starting gene Hackman
Screenshot of Ms. Casey from the TV Show Severance.
The Uruk-Hai from Lord of the Rings. Instead of saying "find the halflings!" he is saying "find the half life!"
A picture of eggs and other food items.
Local newspaper headline: With high egg prices, is it worth raising backyard chickens? What to know in Colorado
"Here's a graph that satisfies the given constraints. The function is positive for − 3 ≤ 𝑥 < − 1 −3≤x<−1 and negative for − 1 < 𝑥 ≤ 3 −1<x≤3. It also increases for − 3 ≤ 𝑥 < 0 −3≤x<0 and decreases for 0 < 𝑥 ≤ 3 0<x≤3, with a local maximum at 𝑥 = 0 x=0. Let me know if you'd like any modifications! ​​ "
An AI generated image of an old dude with a birthday cake that says 1887. The caption says "Happy birthday to Grandpa 1887-2025=-138 years old
A graph showing egg prices going up up and up to 7 dollars per dozen.
Screenshot of Soccer Mommy "Abigail". The video is in the style of Stardew Valley
A timeline showing the 9 blog posts in this series. The timeline is in the form of an arrow going from left to right and has a gradient from blue to orange.
I am holding a black rock over a pot of soaking pinto beans.
Two pots of tamales with a side of sliced green olives
A picture of shredded pork, soaking corn husk and lard, ready to be prepped for tamales
A negroni - a gin drink with vermouth and campairi - in front of a slices orange and a bottle of Jensen's gin
Geoff, wearing a hoodie over a plaid black and white shirt, is holding a card set based on his book, Necessary Conditions . He is in a workroom
The owl from Duolingo telling me I made 597 mistakes this year
Holiday decorations in front of a house depicting classic scenes from Calvin and Hobbes, specifically the scenes with the funny snow sculptures.
Simpsons gif of a scientest talking to Chief Wiggum
Piecewise function created in latex using this code: \documentclass[tikz,border=5mm]{standalone} \usepackage{pgfplots} \pgfplotsset{compat=1.17} \begin{document} \begin{tikzpicture} \begin{axis}[ axis lines=middle, grid=both, xmin=-5, xmax=5, ymin=-3, ymax=5, xlabel=$x$, ylabel=$g(x)$, xtick={-5,-4,-3,-2,-1,0,1,2,3,4,5}, ytick={-3,-2,-1,0,1,2,3,4,5}, tick label style={font=\small}, axis equal, ] % First piece: Nonlinear curve \addplot[domain=-5:-2.1, thick, samples=100] {0.1*(x+3)^3 - 1}; \node[draw, circle, inner sep=1.5pt, fill=white] at (axis cs:-2,-0.9) {}; \node[draw, circle, inner sep=1.5pt, fill=black] at (axis cs:-2,0) {}; % Second piece: Continuous quadratic curve \addplot[domain=-2:2, thick, samples=100] {-(x)^2 + 4}; % Open circle (hole) at (0, 4) \node[draw, circle, inner sep=1.5pt, fill=white] at (axis cs:0,4) {}; % Filled circle at (0, 0) for the second piece \node[draw, circle, inner sep=1.5pt, fill=black] at (axis cs:0,0) {}; % Third piece: Goes to infinity (quadratic growth) \addplot[domain=2.1:5, thick, samples=100] {(x-2)^2 - 2}; \node[draw, circle, inner sep=1.5pt, fill=white] at (axis cs:2,0) {}; \node[draw, circle, inner sep=1.5pt, fill=black] at (axis cs:2,-2) {}; \end{axis} \end{tikzpicture} \end{document}
Screenshot of latex code generated from ChatGPT along with a piecewise graph
A black and white picture of a graph of the function g(x). It is a piecewise function with various intervals. It is mostly nonlinear.
Charles Dance AKA Tywin Lanister
Michelle Goldberg in the NY Times: "I say this as someone who has been called a TERF, a contemptuous acronym that stands for Trans-Exclusionary Radical Feminist, more times than I can count. For a decade now, I’ve been trying to balance a belief in the rights of trans people with my skepticism of some trans activist positions. I’ve written with a degree of sympathy about feminists who’ve been ostracized for wanting to maintain women’s-only spaces. I believe that the science behind youth gender medicine is unsettled, and I dislike jargon like “sex assigned at birth” that tries to mystify or elide the reality of biological sex. (Except for rare exceptions, doctors don’t “assign” sex, they identify it.) I care very little about sports, but it seems dishonest to deny that male puberty tends to confer advantages on trans women athletes."
Screenshot showing the Cavs have had different leading scorers on consecutive games 18 games in
Text of ChatGPT providing functions that don't have rational roots despite the instructions to do so.
Screen shot of calculator showing -1 raised to 2 divide 3 is undefined
The question then becomes: What's the volume of a 216mm-wide pot for every one millimeter of height? Many readers may be struggling to remember their high school (middle school?) geometry formulas, so I'll remind you: The volume of a cylinder is calculated by multiplying pi by the square of the radius, and then multiplying that result by the height. This is the math: Knuckle rice equation Serious Eats Let's just walk through the
Determine the number of solutions to the equation A B − B A = A + B AB where A and B are both integers, −9 ≤ A ≤ 9, and −9 ≤ B ≤ 9.
Screenshot showing an e-book is using my blog post as source material
One of four screenshots showing off mathematical warm ups.
Kamala Harris saying "I love Venn diagrams."
A screenshot of my forthcoming project: Illuminating 6th Grade Math Warm Ups
Flight status showing a 5:04 arrival as "early" (scheduled was 5:05)
Screenshot of "Unpacking"
Screenshot of a headline: A cat just earned his doctorate from a Vermont university
Based on the image you sent, there are 100 circles. There are 10 rows and 10 columns of circles, for a total of 10 x 10 = 100 circles.