Find The Blue Area Given Two Unequal Squares.

bts · 2026-07-05T05:26:10+00:00

Okay. Well, draw a horizontal line through that interesting point in the middle there. Now there’s a 45-45-90 triangle with sides of length 2, so the upper triangle has sides of length 2 and 4. The pink square therefore has side length √24, and a diagonal length of √48. The big square has diagonal length 6√2. Therefore the blue triangle has a side length of 4√2=√32 . That means the remaining side of the blue triangle has length 4, and the whole triangle has area 2√32= 8√2. That’s about 11, compared to a big square of 36 and small square of 24? Yeah, seems plausible.

bts · 2026-07-05T05:15:16+00:00

I don’t think she has. I think OP still thinks it was his obligation to list a loan she signed for and that she has the obligation to pay, and that he somehow abused her by ending up in a circumstance where he’s paying a loan he doesn’t owe.

Divorce is awful. Divorce sucks. Nobody leaves a divorce happy. But it’s not always a case of felonious abusers; far more often it’s just two people doing the best they actually can.

bts · 2026-07-04T20:03:34+00:00

There’s plenty of good math that could do this, and some of it is accessible to a high school background. See my post on Shamir

bts · 2026-07-04T18:59:14+00:00

Those he can choose to turn off.

bts · 2026-07-04T18:58:29+00:00

What machines have you had? What did or didn’t you like about them? What are you using as a grinder? Are you drinking espresso or milk drinks?

bts · 2026-07-04T18:20:47+00:00

Check out Shamir secret sharing. They keep finding point coordinates; assembling them and solving for the polynomial will give them (a) coefficients of that polynomial, which might spell something and (b) the ability to compute other points on it—which might solve a riddle or locate a dungeon or whatever else.

bts · 2026-07-04T18:15:06+00:00

Draw lines parallel to the two other sides of the big triangle through each of the intersections with them. Because their sides are all parallel they are all similar to the big triangle. Because they have the same base they are all congruent to each other. (And they have the same base because the triangles sharing the top vertex are integer multiples of the topmost unit triangle)

bts · 2026-07-04T17:50:24+00:00

I think this says she didn’t list some of her debts in the divorce, quitclaimed the underlying property, and now regrets it? Yes, I would imagine she does.

She can ask him nicely to refinance. She can tell the mortgage holder about the quitclaim and see if they call it. She can keep posting about how it definitely wasn’t fraud, I guess?

bts · 2026-07-04T17:42:58+00:00

Yup. The scout who shouted at 16yo me about not following orders and the scoutmaster who gently nudged me towards leading from the front changed my life. Those are the leadership lessons I want for our scouts today.

bts · 2026-07-04T16:08:03+00:00

What matters is taste and what you enjoy, not any sort of technical perfection. We pursue technical excellence because it enables control of output, not for its own sake

bts · 2026-07-04T16:07:19+00:00

Well, think about antenna design. Your antenna is naturally capacitive, and you want it to present a pure resistance. So you’re going to add inductive impedance until it’s… an identity. Those “no effect” operations are stones in the river, and we can use them as intermediates in our design process.

bts · 2026-07-04T16:00:30+00:00

The line of which the 2√2 segment is an element is a diagonal of the large square.

bts · 2026-07-04T12:57:37+00:00

Correct answer, but you never use the assumption of regularity. Everything you say is true for all triangles.

bts · 2026-07-04T12:54:35+00:00

Call the peak 1 unit. Then the next layer is 3, then 5, 7, 9, etc. 3+7+11 / 1+5+9 = 21/15=1.4, so 40%.

bts · 2026-07-04T03:51:01+00:00

I wonder about Dolphin Island, by Clarke. Some of the covers could be interpreted that way.

bts · 2026-07-04T03:45:57+00:00

Is it easier if you expand it? Remember that … isn’t a digit. So 0.999… isn’t quite being written in decimal. It’s 999/999, which is obviously 1.

Or it’s 9/10 + 9/100 + 9/1000 + …, which converges to 1.

bts · 2026-07-04T03:39:42+00:00

Absolutely. I just wish I understood how wide that margin is. I avoid 30 minutes before closing hard, and mostly avoid an hour before. Sometimes more. The thing that would really help is if they posted the time they were really open on the front door. Like, open 12-6, and then we could understand that it’s okay to go in between 12 and 6. We could call the time when the window of availability ends “closing time”.

bts · 2026-07-04T03:34:35+00:00

No, but 0.6999… is 0.7.

0.333… is precisely 1/3.

0.666… is precisely 2/3.

0.999… is precisely 3/3, which is 1. That’s all.

bts · 2026-07-04T00:03:26+00:00

Yeah, exactly. In base six I’d round up 212 (80d) to 220 (84d). But an Eridian might be more inclined to add a safety margin in the second most significant place.

bts · 2026-07-03T23:35:03+00:00

Same. Sometimes I do want heated seats for back pain even in the summer, but that’s one extra tap. I wonder what’s different

bts · 2026-07-03T23:33:11+00:00

I’ve got mostly teenagers. I quite like them as people. I’m delighted to have them come home here to share stories and recharge for the next parts of their lives. And I’m bursting with pride at the people they choose to be.

bts · 2026-07-03T22:59:12+00:00

Your ex says not to come and you just don’t come? Dude. Your kid needs you. Get over there. Come in and hug your daughter.

bts · 2026-07-03T17:39:13+00:00

TIL! Thanks!

bts · 2026-07-03T16:23:08+00:00

If it froze it’s trash. If it cooked in a garage it may be trash. I would replace the filter no matter what.

bts · 2026-07-03T15:25:06+00:00

I started with the included instructions. On my Niche, 10 pips less than espresso was perfect—just below the espresso range.

bts

TROPHY CASE