nate balk

During one of the worst losing streaks of my career, our team president walked into my office. Keli McGregor. One of the best men I've ever known. He could have come to vent. To question my decisions. To ask hard questions. Instead, he said: "Cut to the chase, Clint. What's next?" I looked him in the eye and gave him two words: "Shower well." The Colorado Rockies were struggling badly that year. Pregame preparation was solid. Scout meetings, early work, attention to detail. All of it was there. But at game time, the tires were flat. I told Keli: the game did everything it could to us today. We just couldn't meet its demands. Now it was time to reset. "Shower well" means exactly this: • Watch the frustration circle down the drain • Shampoo, rinse, repeat and get the grime of today completely off your mind • Walk out clean, go home, and actually rest Leave it at the ballpark. The game is over. There's nothing left to solve tonight. Keli nodded. Asked if he could share it with the whole organization. I said sure. And then it hit me. This isn't just for baseball. Bad day at the office. Grumpy boss. Missed deadline. Traffic on the way home. You can carry all of that through your front door. Or you can shower well. I've never seen a single problem get better because someone dragged it home with them. The reset is a discipline. Same as preparation. Same as showing up. Either we win. Or we learn. The only real loss? When you don't take a single thing out of a hard day. So tonight, whatever kind of day it was, shower well. Tomorrow is a new at-bat. What does your reset look like? I'd love to hear it.

A Favourite: Can you make a three-strand braid with no free ends? Give it a try! (Notice how each strand is relatively flat.)

A Challenge: Can you make a four-strand braid with now free ends? Give it a try! (Notice how each strand is relatively flat.)

12 toothpicks: There are 12 ways to split into three non-empty piles and exactly one-quarter of those examples make the sides of a triangle. What's the next number N for which exactly 25% of the piles of three you can make form a triangle?

Mathematics. "The Zero's Journey." By Grant Snider, @grantdraws, incidentalcomics.com, Used with permission.

I desperately need to know if Mike ad-libbed all that or if he’s using the prompter. Either way, it’s one of the all-time great closes to a sporting event I’ve ever seen. It resonated deeply with the audience. If he did that off the top of his head, crown him now. Wow.

There is only 1 way to "split" a pile of N coins into one pile. There are N/2, rounded down to the nearest integer, ways to split them into 2 non-empty piles. (Order of the piles irrelevant.) Prove there are (N^2)/12, rounded to the nearest integer, ways to split into 3 piles!

A meta-analysis of elite Olympic athletes (top 16 in the world) found they: • Started their sport at 10 years old • Focused on their sport at 15 • Skiing, soccer, basketball, and hockey players sampled other sports for 7 years The authors concluded: “Only after the age of 12 should the volumes of deliberate practice increase so that an athlete can specialise in one sport.”

Is the transition below smoothly transforming an a-b-c triangle into a d-e-f triangle too naive? Could an intermediate phase not actually be a triangle?

Quickie: One can smoothly transform a 3-4-5 triangle into a 4-4-4 triangle with intermediate (3+k)-4-(5-k) triangles preserving perimeter along the way. (k transitions from 0 to 1.) The top vertex of the triangle moves along a section of a curve. What curve?

It is known that the three altitudes x,y,z of a triangle satisfy 1/x +1/y > 1/z, 1/y + 1/z > 1/x, and 1/z + 1/x > 1/y. If three numbers x, y, z meet these conditions, must there be a triangle with these lengths for its altitudes?

@dmarain @HarMath @decompwlj @mATH_e_matics @ybgoi @RaminKhosravi4 @JohnAllenPaulos A visual proof 😉

Looked at some old writings. Wondering how I came up with the numbers 4, 6, 12 to make this puzzle solvable. Hmm! What other values for speeds work for this puzzle? (3,5,15, yes!, 2,5,10, no!) [Assume the path is composed of clearly-defined uphill, downhill, and flat sections.]

The triangle shown with one side in red and its third corner on a dot has an even number of dots (6) on its boundary. Pick any other dot and use the red side and that dot to make a triangle. It too will have an even number of dots on its boundary! Why must this be so?

Entertaining Mathematical Puzzles by Martin Gardner PDF: abrarhashmi.wordpress.com/wp-content/upl…

Explain why every triangle with one side the red edge and third corner on a dot is sure to have area a whole number of square units. (Here, 1 square unit is the area of one small square of dots.)

Dots on a square lattice, each colored one of four colours in a regular pattern as shown. Pick a starting dot. Pick any "leap-over dot" and leapfrog over it to land at a new dot. Repeat over and over. Are you sure to stay on the same starting colour as you leapfrog about?

Today's Thought rather than a Puzzle: The school curriculum is shaped by a fundamental tension: while much of mathematics is motivated by real‑world intuition, the mathematics that emerges ultimately outgrows any single model that inspired it. corwin.com/books/math-dec…