Wow! That’s way better than my multiplying by the conjugate way.
28.02.2026 01:32
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Wow! That’s way better than my multiplying by the conjugate way.
Thanks for sharing!
Only ever used it in an upper division Astronomy class with spherical trig. By that time, it was a trivial calculation to pick up if you had never seen arcminutes. I skip it in pre-Calc unless I have extra time.
Love it! Keep ‘em coming!
Vector field F=<y-x, -x-y> has been overlayed onto a snail shell. The vectors point in the direction of the spiral of the shell.
Student has taken a picture of a rift in the ground and overlayed a vector field where the vectors approach the rift generally at right angles and then turn into the rift and crash out pointing down.
Image is a subsection of Van Goghs Starry Night. It’s the large whorl in the sky. Over the image is a vector field which points along the whorl. The vector field is -sin(x-y) for the i component and cos(x+y) for the j component. The vector field is handwritten. The image is black and white.
The vector field F=<x,2-x^2> is overlayed on the image of a fountain in a pond. The water sprays straight up and falls down into a circular region. The vectors point along the motion of the water.
Vector fields as art. In #MathsToday the students had to create a vector field and overlay it with a picture to create Vector Art.
Just a fun little extension at the end of a unit. #iTeachMath
This looks fun. Do you have a link you can share for the document?
What a great idea!
Last challenge was to use at least 3 logs to create log8. Students were really creative. But the fact that one group had log2+log2+log2 and another had 3log2 helped move towards the log(2^3)=log8.
It was a nice way to informally introduce log properties and play with log tables b4 formalizing.
In #MathsToday we had success discovering the log properties. I had students use a log table to find all the ways to combine logs to equal log2, which led to them noticing the loga-logb=log(a/b) property. Then they looked for ways to make log12 (which led to discovering the product property.
Fire and Ice!
Your prompt has really gotten me thinking. I’ll have to share it with some students and see what they come up with.
A square divided into 4 rectangles each n by n+1 in dimensions arrayed around one digit at the center. My attempt to show a visual proof that and odd square number is one more than a multiple of 8.
Or perhaps this visual I made on Polypad showing the 4 copies of the product of consecutive numbers.
A visual proof that an odd number squared equals 8 times a triangular number plus one. This image is a 9 by 9 grid with the center square colored purple. The remaining squares are broken into 8 equal triangles of 10 and colored to look like a pinwheel. So 81 = 9^2 = 8(10)+1.
A neat extension seen on Facebook. A visual proof that an odd number squared is also 8 times a triangular number plus one.
You can modify the prompt and get a second problem. How many different slopes can there be for segments connecting grid points? How does that change with the grid size?
I applied.
Wait… I thought all cows were spherical….
A picture of the previously described map
I only have a small printer at home. But here it is! It’s on the fridge so the teen will see it and ask about it. 😀
Thanks! I’m printing the knot map out now…
I had the same thought about the poster.
That is beyond sweet! Happy birthday.
I’m enjoying following along on your blog too.
Student whiteboard work which shows an attempt at drawing the Koch snowflake. Start with a triangle, divide each sides into thirds, and replace the middle third with a new equilateral triangle, then repeat. Below the Koch Curve is a table which records the number of sides in column one, the length of a side in column 2, and the third column will hold the perimeter, but is currently empty. The rows represent the iteration. Below the table the students are working on are some multiplication calculations.
Student white board work shows a table with the following columns; stage number, number of sides, side lengths, and perimeter. The stage nUmber column contains 0, 1,2,3,n. The number of sides column contains 3,12,48,192 and the function 3(4^n). The side lengths column contains 1,1/3,1/9,1/27, and the function 1/3^n. The perimeter column contains 3,4,48/9,7 (sic), and the function 3(4^x)/(3^n).
In #MathsToday we used the Koch Snowflake to review writing exponential equations from data. Students then discussed what the end behavior would be for the equation of the perimeter.
The kids enjoyed hearing how this was thought “abominable” by mathematicians when first discovered.
How timely. We are doing this lesson tomorrow!
In #MathsToday we learned how to sketch vector fields. Then we had some fun with this neat app. Try the randomize button. #maths #MathArt
anvaka.github.io/fieldplay/?c...
I want to be in your class!!
In AP Calculus, calculators are used to approximate definite integrals for functions with unknown antiderivatives. They are also used to approximate zeros for more complicated functions.
Open cubes look fun. Did you create every possible type?
That looks so cool!
