u/i12drift

I was teaching the very beginnings of the idea of how to find the slope of a tangent line at (1,1) for the function f(x) = x^2 last Thursday.

We did it by 'creeping' up to x = 1 from both ends, like.. Idk it's hard to describe without my mouth or the ability to write on a whiteboard.

"We could hold the point (1,1) fixed and 'drag' the point (3, 9) to the left towards (1,1) until we got really close, like (1.01, 1.0201), and find the slope between those two points. That would be a really good approximation."

*makes table with x = 1.2, 1.1, 1.01*

"We could do the same from the under-side as well. Hold (1,1) fixed and slide (0,0) up and right really close to (1, 1), like (0.99, 0.9801) and find that slope."

Q: What does it appear the slope should be?

Class A: "It looks like the slope should be 2!

But then a student of mine asked a fun question: What if we took a point on either slide and slid both of those towards (1,1)? Would that work?

I had to pause for a bit and think about it. My answer was that having two moving parts might be a bit more cumbersome than needed, but yes it should work.

A few days later (today), the thought popped back into my head, so I did it. It works and it's simple and it's cool.

Before going to redrocks, I bought some new weight savings items cuz im a nutter-butter and felt like blowing my promotion/retention bonus on superfluous climbing gear. It was definitely noticeable.

We were going to do Epinephrine but opted not to cuz we didn't wanna wake up mega early. Instead, we flew in and did Birdland on day1, Johnny Vegas into Solar Slab on day2, and then The Great Red Book + fly out on day3.

Without going into the nitty gritty details, my multipitch gear swaps/changes led to:

• 4x less alpine carabiners = 132g reduction
• 8x 60cm slings --> 7x lighter 60cm slings = 50g reduction
• 2x 120cm slings --> 2x lighter 120cm slings = 16g reduction
• 1x 240cm sling + 2x HMS --> lighter 240cm + 1x HMS = 77g reduction
• A few cam swaps = 63g reduction (already owned, just optimized what was brought)
• 16x lighter cam carabiners = 78g reduction
• rappel device + carabiner swaps = 37g reduction
• lighter harness = 160g reduction
• no more personal anchor = 172g reduction
• 5x extra carabiners (lol) --> 1x extra carabiner = 147g reduction
• nuts + nut tool change = 88g reduction

My gear's weight went from 11.75 pounds to 9.5 pounds; A 2.25 pound reduction!

Megan participated in the 'weight loss' shinanigans by swapping from her 3,990g Sterling 70m rope to a 3360g 70m Beal opera; Another 1.33 pounds.

Individually, each piece of gear swap felt minor, but they all added up to a noticable difference. We both agree we didn't notice the rope weight difference except for during the approach.

We're all familiar that cams vary in size from company to company. Cam-parison.com illustrates that pretty well.

I think I found a pretty good mix of cams and sizes to optimize the most overlap between sizes for the companies I like to use (BD, WC, DMM, totem). For example, a red dragon is the smallest red cam, and the wild Country friend is the biggest red cam.

EDIT: I posted the wrong picture, but it's basically what I wanted. I use a blue totem, not a BD C4 0.3, and BD #3, not the dragon. Here's the link to what I found to be what I think is optimal.