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Arsenal fan, FPL enthusiast @oxunimaths student, @teachfirst maths teacher

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@Mike_kim714 @Titleist 32

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@Mike_kim714 @Titleist 52

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@catrionateaches One of my students today coined this the “Robin Hood method” to take from the rich and give to the poor

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@runningstitch @MrLeeBates You say ratio tables are great but formula triangles are not, but they are mathematically equivalent in a way :

/A\ ~ A|B
/B|C\ ~ C|1

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@blatherwick_sam Something to do with 0.911 maybe?

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@GeoFreC @jamestanton The method doesn’t work for this, a rotation is needed after

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@GeoFreC @jamestanton

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@Tomboktu @jamestanton No, consider a line (really thin rectangle)

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@jamestanton Drawing a line from a vertex, for each L (below) we have a point where A=B by IVT on A-B
Plotting these points from top to bottom we can see that there will be a point where A=B=C by IVT again on C-A

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@jamestanton If the point is the centre of mass then if the regions are labelled a,b,c,d clockwise then a+b=c+d and b+c=a+d
Now, if a=b we are done
Otherwise rotate around the centre of mass until a-b=0 which will happen due to the IVT

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@jamestanton The tetrahedron (a triangle with a central dot is not 2-colourable)

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@edsouthall If we assign a direction to the closed loop, we must have sum(>)=sum(<)=3+5 and sum(^)=sum(v)=5
So sum(<,^,>,v) = 8+5+8+5=26

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@catrionateaches @Whitehughes @Trudgeteacher @mathforge @DavidKButlerUoA This one is nice to prove the squared trig identities from

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@mathsteacher09 Is this not an isosceles triangle?

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@Whitehughes A scalar with a unit is a 1-dimensional vector; changing the basis corresponds to changing the unit.
Displacement is a vector but…
My thought now is that the unit is the vector part and s is the scalar? But am becoming less sure about this the more I think about it!

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@Whitehughes I have thought about my first answer and it’s not we don’t underline in 1d it’s just we don’t write our vectors! We could define a direction and magnitude of a unit vector but normally that is implied in the question by the direction and unit

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@Whitehughes The confusion in 1d is that the scalars and vectors are both 1 dimensional and lie in R so we don’t underline
In 2 or more dimensions the vectors (in R^n) have more dimensions than the scalars (in R) and so we underline to define the difference between the two

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@tm_maths It kinda ends up looking like a circle theorems question, using the inverse of angle subtended by a chord and angles at centre

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@MoritzSchauer @JDHamkins I guess taking points in an arbitrarily small mesh would give rational values by a density argument but I’m not sure whether that is what you’re asking