Genady

And another AI fail. A meaningless "solution": ### Steps to Construct Point C (Midpoint of A and B) Using Only a Compass: 1. **Draw a circle centered at A with radius AB:** - Place the compass at point A and adjust its width to the distance AB. - Draw a circle centered at A with radius AB. 2. **Draw a circle centered at B with radius AB:** - Without changing the compass width, place the compass at point B. - Draw a circle centered at B with radius AB. 3. **Find the intersection points of the two circles:** - The two circles will intersect at two points. Let’s call these points P and Q. 4. **Draw a circle centered at P with radius PA:** - Place the compass at point P and adjust its width to the distance PA (which is equal to AB). - Draw a circle centered at P with radius PA. 5. **Draw a circle centered at Q with radius QA:** - Similarly, place the compass at point Q and adjust its width to the distance QA (which is also equal to AB). - Draw a circle centered at Q with radius QA. 6. **Find the intersection points of the new circles:** - The circles centered at P and Q will intersect at two points: one of these points is A, and the other is the midpoint C. 7. **Identify the midpoint C:** - The intersection point that is not A is the midpoint C between A and B. ---

I've found that the last problem can be solved also by using intersections of circles, i.e., circles crossing rather than touching at points. It can be done by following constructions in the proof of Mohr–Mascheroni theorem - Wikipedia. Although, these constructions are very long and convoluted.

Saying that the emergence of life was "guided" puts them squarely into the "divine intervention" camp.

Good, but this is not the problem that led to the question in the thread. Here is a solution of this problem: Now, the problem in question is this: Given points A and B construct point C in the middle between them using only compass. I've solved this problem, but my solution relies on being able to mark a point where two circles touch rather than cross each other. I don't know if this is legitimate. That was why I've asked.

I should just formulate the original problem, and all will become clear: Given two points, A and B, construct a point C, using only a compass, such that B is a midpoint between A and C.

Yes, but as I've clarified in the post before yours, I don't have a centerline, or any line, because I don't have a ruler. If I had ruler, I would use it only as a straightedge, i.e., in the classical meaning. The circle is drawn, and its center is known, so it is not a problem to take its radius with compass. Then, the diameter can be constructed by doubling the radius, which is doable with compass only, i.e., no ruler is needed for this.

Even more specifically... With ruler and compass I could construct the point where the circles touch as a point where the line connecting their centers cross them. However, what I deal with is a construction using compass only, no ruler. I don't know if constructing that point by crossing only some circles is possible.

In classical constructions with ruler and compass, a construction proceeds from point to point where the points are intersections of lines and circles, i.e., where the lines and the circles cross each other. Are the points where the lines and the circles touch each other rather than cross, allowed as well? More specifically, if I have constructed two circles and I know that they touch at some point, can I proceed with the construction using this point?

Fair enough.

Do you think it is possible that they ask a question in a math test about something that has not been defined?

It takes 1 hour.

Not only its answer is wrong, but also its first statement: because a semicircle is rather one-dimensional. Incidentally, I've just read that this AI, DeepSeek, (Tech leaders respond to the rapid rise of DeepSeek | VentureBeat). So, they are all that bad. P.S. It seems that you think I brought the AI answer as a correct one. Clearly, there is a miscommunication, because my intent was exactly opposite. P.P.S. I make mistakes in English from time to time, but I do not translate from Russian.

I don't know why it would matter, unless they were taught something wrong. I also don't see anything tricky about the question. They are given a figure, which consists of a semicircle, a line, and an area, and they need to answer the question about the semicircle.

This is one unknown, and you get one equation. Then solve the equation.

Do you need the integrals? The volume of the cone between the two cuts plus the volumes of the two domes equal 2/3 pi r^3. The formulas for all these volumes are known.

Calculate them separately, e.g., The spherical dome: Surface area and volume

I don't think the remaining part of the sphere matters at all. You need to express the volume of the part cut out by the cone and make it equal 2/3 pi r^3.

Being misled by a visual is not a necessary condition for answering the question wrong, evidently. For an experiment, I gave the question, with no diagram, to AI: How many corners does a semi-circle have? AI has picked this answer: A semicircle is a two-dimensional shape that represents half of a circle. It is formed by cutting a whole circle along its diameter. When considering the number of corners (or vertices) a shape has, we typically look for points where two straight edges meet. A full circle has no straight edges and thus no corners. However, a semicircle includes the diameter as a straight edge. Here's the breakdown: The curved part of the semicircle is smooth and has no corners. The straight edge (the diameter) connects two endpoints. Therefore, a semicircle has two corners, which are the two endpoints of the diameter. These points are where the straight edge meets the curved edge, forming vertices.

It was bad last time, I remember. They were detaining people in airports for idiotic reasons. I have canceled then my trip to the US with my wife, and lost hundreds of $$, because my passport says that I was born in Azerbaijan, which certainly sounds like a Muslim country.

But the question was about "a semi-circle." It's a math question. It is rather a student who "seems to miss that what is actually pictured is a partial disk and not a semicircle."

Because of the verbiage like this ^^^^, I think that by "abiogenesis" he means "spontaneous generation". Which it is not for a long time by now.

No, such definition is not necessary.

No, it is not. It is a dimensionless number. To help me understand this question, please answer this one: number 3, is this a "mathematical" construction, or does it have a physical meaning.

Re 'math for masses'... What do you think about this elementary math question: (Student's answer to math question sparks discussion after teacher marks it as incorrect - Scoop Upworthy)

OK. Good luck!