Dave Richeson

"There's no Royal Road to geometry." —Euclid to Ptolemy (according to Proculs) "O king, for traveling through the country there are private roads and royal roads, but in geometry there is one road for all."—Menaechmus to Alexander the Great (according to Stobaeus) I've been thinking about this

that Herodotus wrote, "There is nothing in the world that travels faster than these Persian couriers...Neither snow nor rain nor heat nor gloom of night stays these couriers from the swift completion of their appointed rounds." And that is the source of the famous statement about US Postal

"There's no Royal Road to geometry." —Euclid to Ptolemy (according to Proculs) "O king, for traveling through the country there are private roads and royal roads, but in geometry there is one road for all."—Menaechmus to Alexander the Great (according to Stobaeus) I've been thinking about this

quote (with competing attributions) while talking to my students about the importance of "the struggle" when doing math. It is tempting to go straight to AI or an answer key, or to skip the ungraded/uncollected problems. Doing math is the best (and often only) way to learn math. One can often be

I'm no expert in any of this, but... YIKES!!! "A normal size for a NIST P-384 elliptic curve cryptography private key contains roughly 384 bits of entropy, a size allowing almost 2³⁸⁴, or a number with 116 digits, different possibilities. The private key sizes of the compromised keys ranged from

“Squaring the circle”— A circle made with square pixels and a square made with circular ones. I’m trying to decide which effect is better, showing both sides or showing one side from two angles. 

Here's my latest visual illusion. I came up with the idea while walking the other day. It is a 3D-printed sheet with holes cut so that it looks different from two different directions, or when light is shone through. What do you think? Spooky? 1/3

The cat-spider illusion.

This is an impossible task: selecting "the nine records that shaped your taste." These are not my favorite albums—they aren't even my favorite albums by these artists. They are albums that changed the kind of music I listened to. Make your own grid at my9albums.org

I just learned this beautiful result by Edeman, Kostlan, and Shub (1994): For an n×n random matrix with random (independent standard normal) entries, the expected number of real eigenvalues E_n satisfies E_n/sqrt(n) → sqrt(2/π) as n → ∞. So E_n grows like sqrt(2n/π) ≈ 0.798·sqrt(n).

I wanted to see how my calculus students could do creating a closed piecewise parametric curve for an impossible object. They made one side and could choose one of my shapes for the other side. Then I printed the objects. It went well, and I think I can ramp it up a little bit and

Math professor poll: When you teach calculus, do you allow students to bring a notecard/formula sheet? a. No. They have to remember everything b. Yes, one 8.5"x11"/A4 sheet c. One note card d. I provide formulas e. Other

So... I just saw there's a film about the Unabomber coming out tomorrow... And it stars John Nash... I mean, Russell Crowe. www.imdb.com/title/tt6933... In all seriousness, I was in grad school at Northwestern when the Unabomber was caught, and Northwestern math professor Don Saari pointed said

I had a student ask the other day why we don't multiply vectors in the expected way (component-wise). So, <a,b,c>⊙<d,e,f>=<ad,be,cf>. My gut response was that we could, but it isn't as useful as the dot product or the cross product. But I decided to think about it and see if I could come up with 1/6

|v||w|sinθ, and so on. I then gave an example of two vectors v and w and a 90° rotation R about the y-axis yielding vectors R(v) and R(w). All of the familiar operations "played nice" with the rotation. For instance, for the cross product, R(v x w)=R(v)xR(w) and for the dot product 5/6

I had a student ask the other day why we don't multiply vectors in the expected way (component-wise). So, <a,b,c>⊙<d,e,f>=<ad,be,cf>. My gut response was that we could, but it isn't as useful as the dot product or the cross product. But I decided to think about it and see if I could come up with 1/6

v⊙w gives the value you own in each stock. But what differentiates the Hadamard product from the other vector operations we talk about in Multivariable Calculus—addition, subtraction, scalar multiplication, the dot product, and the cross product—is that it is not a **geometric** operation. We 3/6

I had a student ask the other day why we don't multiply vectors in the expected way (component-wise). So, <a,b,c>⊙<d,e,f>=<ad,be,cf>. My gut response was that we could, but it isn't as useful as the dot product or the cross product. But I decided to think about it and see if I could come up with 1/6

Today in Multivariable Calc, I mentioned the connection between the cross product and quaternions. So I showed them a photo of me with the Hamilton plaque in Dublin from this summer!

Over the weekend, I had an idea: what if, instead of the objects appearing to sit horizontally in front of you, I modified them to appear vertically? Here are four test attempts.