1. Passing tests—in a geometry class, taking the ACT, (I don’t know, maybe it’s a part of getting a GED).
2. Your interest in geometry is not merely theoretical, but practical. Maybe you construct things, perhaps out of wood using power tools. (You may find it useful to design/implement a coordinate system on a piece of wood to assist with getting the dimensions of things right, as you cut them out with a saw. Someone may have already invented this.) If you are trying to find the area under a curve, you may find it useful to buy very fine, high quality paper, graph the shape of the curve, and weight it, and use the average wight of the paper per inch or centimeter (squared) to find the answer. (This relies of the material being consistent through out, and weighing about the same everywhere.)
3. Despite your claims that you would never use math, or this part of math, someday you find yourself* designing a dome, or even a half sphere, perhaps as a place to live. The floor plan is a circle.
4. You enjoy math. You enjoy learning this/using this knowledge on puzzles to challenge your wits. (See 6)
5. You end up as a teacher, assistant, or tutor. The subject is math. (Perhaps you realize that not every geometry student that will one day teach geometry is aware of this fact.) Whether or not you learned all the fancy stuff the first time, if you didn’t retain it you have to learn it again—well enough to teach it to someone that doesn’t like the subject as much as you—and you hated geometry (class). (It was required.)
6. You learn visual calculus. Other mathematicians may compose long, elaborate arguments that they publish in papers that may take days to decipher (that seem to push the world ever closer to proofs people can’t read, but computers have apparently checked—or been used to produce). Perhaps your proofs employ no words, but consist of a picture instead, that employs esoteric knowledge (such as that of tangents and chords) to solves problems beautifully (and quickly). Perhaps this profound knowledge makes you both a better mathematician, and a better teacher of math.
In summary:
It’s arbitrary, but it’s part of the curriculum that’s tested on. (However students or teachers feel about it.)
You use the knowledge—specifically*, or generally**.
You enjoy learning, or a challenge.
Teaching.
“Higher math.” (You can see more up here, but the air is thinner. You feel kind of dizzy.)
*Your life has turned into a geometry problem. Is this hell?
**The square-cube law is general and useful. I think the second property is a result of the first.
Possible uses:
1. Passing tests—in a geometry class, taking the ACT, (I don’t know, maybe it’s a part of getting a GED).
2. Your interest in geometry is not merely theoretical, but practical. Maybe you construct things, perhaps out of wood using power tools. (You may find it useful to design/implement a coordinate system on a piece of wood to assist with getting the dimensions of things right, as you cut them out with a saw. Someone may have already invented this.) If you are trying to find the area under a curve, you may find it useful to buy very fine, high quality paper, graph the shape of the curve, and weight it, and use the average wight of the paper per inch or centimeter (squared) to find the answer. (This relies of the material being consistent through out, and weighing about the same everywhere.)
3. Despite your claims that you would never use math, or this part of math, someday you find yourself* designing a dome, or even a half sphere, perhaps as a place to live. The floor plan is a circle.
4. You enjoy math. You enjoy learning this/using this knowledge on puzzles to challenge your wits. (See 6)
5. You end up as a teacher, assistant, or tutor. The subject is math. (Perhaps you realize that not every geometry student that will one day teach geometry is aware of this fact.) Whether or not you learned all the fancy stuff the first time, if you didn’t retain it you have to learn it again—well enough to teach it to someone that doesn’t like the subject as much as you—and you hated geometry (class). (It was required.)
6. You learn visual calculus. Other mathematicians may compose long, elaborate arguments that they publish in papers that may take days to decipher (that seem to push the world ever closer to proofs people can’t read, but computers have apparently checked—or been used to produce). Perhaps your proofs employ no words, but consist of a picture instead, that employs esoteric knowledge (such as that of tangents and chords) to solves problems beautifully (and quickly). Perhaps this profound knowledge makes you both a better mathematician, and a better teacher of math.
In summary:
It’s arbitrary, but it’s part of the curriculum that’s tested on. (However students or teachers feel about it.)
You use the knowledge—specifically*, or generally**.
You enjoy learning, or a challenge.
Teaching.
“Higher math.” (You can see more up here, but the air is thinner. You feel kind of dizzy.)
*Your life has turned into a geometry problem. Is this hell?
**The square-cube law is general and useful. I think the second property is a result of the first.