THIS is why cleaning is so difficult.
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@futurebird now I’m trying to think how to use a compass to put the square root of two on a ruler. Feels like I should be able to worl that out.
Can you use a compass to make a square?
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THIS is why cleaning is so difficult. I bought these blank ruler-sized pieces of wood six years ago. I have an idea for a lesson where students use a compass to create a ruler, including irrational numbers, such as square root of two I should write the lesson up and make the sample ruler **or** throw these away. I will write myself a note about this and put them in the “soon trash” box. I need to be ruthless!
@futurebird
Or, drill a hole in one end, attach a string & make bullroarers out of them?
https://en.m.wikipedia.org/wiki/Bullroarer -
In fact I will take these to school and make it THEIR problem. I have a whole box of materials and notes for possible future lessons, and if I put them all in one place I'll be more likely to get them written up and ready to go so other teachers might use them.
I've told the other math teachers about how we should do this and they sort of nod along but I suspect they have no idea what I'm talking about.
But if I show them a ruler with root two on it it'll be clear enough I think.
The whole idea of the lesson, which I'm very passionate about is making irrational numbers like root two and root three seem... real. Both as "real numbers" but also as ... real numbers, physical distances that make as much sense as 4 cm or 1/3 of an inch.
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@futurebird
Or, drill a hole in one end, attach a string & make bullroarers out of them?
https://en.m.wikipedia.org/wiki/BullroarerThat's a good idea. I have them make right angles using "the Egyptian method" by tying knots and this would be a nice way to store that device after you make it.
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F myrmepropagandist shared this topic
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The whole idea of the lesson, which I'm very passionate about is making irrational numbers like root two and root three seem... real. Both as "real numbers" but also as ... real numbers, physical distances that make as much sense as 4 cm or 1/3 of an inch.
@futurebird Also, slide rules (some marking needed).
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The whole idea of the lesson, which I'm very passionate about is making irrational numbers like root two and root three seem... real. Both as "real numbers" but also as ... real numbers, physical distances that make as much sense as 4 cm or 1/3 of an inch.
@futurebird YEAH!! YEAH!! THIS IS RADICAL!! There's literally nothing that says we can't put algebraic numbers on a ruler!!
Slide rules already do this with e and pi and conversion factors to/from arcminutes and arcseconds!
What I'd love to see is a "complex ruler". A combination ruler and protractor that can "measure" a complex number in its polar form (slightly more advanced than studying them in cartesian form, but makes them A LOT easier to conceive as actual numbers imho)
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@futurebird Also, slide rules (some marking needed).
@futurebird You probably know it already, but just in case —
before modern slide rulers were invented, Napier literally sold multiplication sticks, marked with discrete integers.
Napier's Bones -- from Wolfram MathWorld
Napier's bones, also called Napier's rods, are numbered rods which can be used to perform multiplication of any number by a number 2-9. By placing "bones" corresponding to the multiplier on the left side and the bones corresponding to the digits of the multiplicand next to it to the right, and product can be read off simply by adding pairs of numbers (with appropriate carries as needed) in the row determined by the multiplier. This process was published by Napier in 1617 an a book...
(mathworld.wolfram.com)
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THIS is why cleaning is so difficult. I bought these blank ruler-sized pieces of wood six years ago. I have an idea for a lesson where students use a compass to create a ruler, including irrational numbers, such as square root of two I should write the lesson up and make the sample ruler **or** throw these away. I will write myself a note about this and put them in the “soon trash” box. I need to be ruthless!
@futurebird
dinosaurs are planning to rule the world again and I think if you're not using these rulers for anything important, you should donate them to the dinosaur cause. -
The whole idea of the lesson, which I'm very passionate about is making irrational numbers like root two and root three seem... real. Both as "real numbers" but also as ... real numbers, physical distances that make as much sense as 4 cm or 1/3 of an inch.
@futurebird I love this. They can also practice geometry as they make it.
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THIS is why cleaning is so difficult. I bought these blank ruler-sized pieces of wood six years ago. I have an idea for a lesson where students use a compass to create a ruler, including irrational numbers, such as square root of two I should write the lesson up and make the sample ruler **or** throw these away. I will write myself a note about this and put them in the “soon trash” box. I need to be ruthless!
How can you put an irrational number on a ruler ?
I mean, boundaries for the number I get, but the number itself ? -
How can you put an irrational number on a ruler ?
I mean, boundaries for the number I get, but the number itself ?Make a square that is 1cm by 1cm then use a compass to mark the diagonal on the ruler at root 2cm
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@futurebird I love this. They can also practice geometry as they make it.
@mathcolorstrees @futurebird Oh hey not to butt in like an idiot (butts in like an idiot) but yesterday someone posted something titled ‘geometric shapes’ and I wondered
Are there any non-geometric shapes? -
Make a square that is 1cm by 1cm then use a compass to mark the diagonal on the ruler at root 2cm
Isn't that luring the kids ?
The size of the mark will be the boundaries, but IIRC there's no way to put the exact number on the ruler. -
Isn't that luring the kids ?
The size of the mark will be the boundaries, but IIRC there's no way to put the exact number on the ruler.Well in that sense you can't make a ruler for ANY number.
It's as good as any other mark you might make on the ruler done this way IMO.
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The whole idea of the lesson, which I'm very passionate about is making irrational numbers like root two and root three seem... real. Both as "real numbers" but also as ... real numbers, physical distances that make as much sense as 4 cm or 1/3 of an inch.
@futurebird
I wonder if it would be more effective to get blank 45 45 90 triangles and label the hypotenuse in terms of √2 ?Unfortunately that's probably harder.
That said - I think I've seen circle and a matched tape labeled in terms of π . A choice of radiant beauty.
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@futurebird You probably know it already, but just in case —
before modern slide rulers were invented, Napier literally sold multiplication sticks, marked with discrete integers.
Napier's Bones -- from Wolfram MathWorld
Napier's bones, also called Napier's rods, are numbered rods which can be used to perform multiplication of any number by a number 2-9. By placing "bones" corresponding to the multiplier on the left side and the bones corresponding to the digits of the multiplicand next to it to the right, and product can be read off simply by adding pairs of numbers (with appropriate carries as needed) in the row determined by the multiplier. This process was published by Napier in 1617 an a book...
(mathworld.wolfram.com)
everybody knows
about Napier's bones
you could multiply
and you could divide
you could even extract
the square root
such sweet sweet necromancybut nobody knows about
Genaille–Lucas rulers
with which you could save
a little addition on the way
at the price of a
much more complicated name
and no allusion
to death
and what the dead might say
