Vincent Pantal🍩ni

Math & animations with GeoGebra 🇫🇷 • Once a teacher... • Author w/@edsouthall of #GeometrySnacks (and More G.S.) • #mathGIF
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[Vincent Pantal🍩ni @panlepan]

I made a thing. One shape fits all.

[Vincent Pantal🍩ni @panlepan]

@pickover Nice! I think this is even better to see y=sqrt(x) !

Explain why for every even integer n, sqrt(n) can be read at the intersection of two semi-circles.

[Vincent Pantal🍩ni @panlepan]

@pickover Nice! I think this is even better to see y=sqrt(x) !

Explain why for every even integer n, sqrt(n) can be read at the intersection of two semi-circles.

[Vincent Pantal🍩ni @panlepan]

@H0H0v b) As Donald Knuth puts it in "Concrete Mathematics" about the Stern-Brocot tree, one can consider that 1/0 is infinity in its lowest form. :)

[Vincent Pantal🍩ni @panlepan]

@PaulaKrieg @geogebra Same here... Twitter has gone so wrong I hardly come over here anymore but I do miss the good ole days where math/arty people would share their ideas and chat about it.

[Vincent Pantal🍩ni @panlepan]

@engineer_know With @geogebra

[Vincent Pantal🍩ni @panlepan]

Regular hexagon on a cube unfolds in a straight line on this net.
#MathGIF #GeometrySnacks

[Vincent Pantal🍩ni @panlepan]

@1939worldsfair Ohh that's nice ! I was looking for such a puzzle but didn't see the congruent triangles, thanks !

[Vincent Pantal🍩ni @panlepan]

#SundayPuzzle.
A red right-angled triangle and its incircle. Prove that the blue rectangle has the same area than the red triangle.
#GeometrySnacks

[Vincent Pantal🍩ni @panlepan]

@AmareshGS1 Nice. Thanks for sharing. Knowing r=(a+b-c)/2 helps!
I'll share a proof without any calculation eventually. ;)

[William Rose @dodecahedra]

Like an hour ago, my kids decided they were mathematicians and began a series of investigations (on their own).

1+2+⋯+10=55
11+12+⋯+20=155
21+22+⋯+30=255
etc.

They conjectured the general theorem. Pretty exciting.

[Vincent Pantal🍩ni @panlepan]

@WhiteHouse Are these real people ?
I thought the picture was taken in a shitty wax museum.

[Vincent Pantal🍩ni @panlepan]

@mikeandallie Things have changed around here, but this is still valid. :)

[Vincent Pantal🍩ni @panlepan]

A nice proof without words of the Pythagorean Theorem by Abu' l'Hasan Thâbit ibn Qurra Marwân al'Harrani (826-901) with 6 congruent 📐.
The total area 𝓐 can be seen in two ways :
1⃣ 𝓐=🟥+ 3 📐
2⃣ 𝓐=🟩+🟦+3📐
So 🟥=🟩+🟦
@CutTheKnotMath proof #24
https://t.co/X9HdcJXDa9

[Robert Fathauer @RobFathauerArt]

5-stars were commonly used on the ceilings of tombs and other buildings in Ancient Egypt to depict the heavens. They are usually not connected to one another, but they are connected in this ceiling in the Ptolemaic Denderah Temple to form a sort of tessellation.

[Vincent Pantal🍩ni @panlepan]

@DefiantLs

[Vincent Pantal🍩ni @panlepan]

@_Manuel_Ruiz_ @jamestanton Nice. It's surprising at first because from this figure you could think T(2n)=4Tn but when you try to do it with the dots, it doesn't work...

[Vincent Pantal🍩ni @panlepan]

@jamestanton Congrats James !

[Vincent Pantal🍩ni @panlepan]

@asitnof Nice puzzle. I still don't see why the two dotted pieces have the same area...

[Vincent Pantal🍩ni @panlepan]

#Puzzle 📐Prove that the yellow right triangle, the pink rectangle and the cyan square all have the same area.
#GeometrySnacks

[Vincent Pantal🍩ni @panlepan]

@AmareshGS1 Well done ! You can also see that :
(a-r)(b-r)
=ab-[(a-r)r+(b-r)r+r²]
=ab-Area(ABC)
=Area(ABC)

[Vincent Pantal🍩ni @panlepan]

@mnd233445 The areas of the three triangles can be measured as fractions of ABC's area S:
a=S/15,
b=S×3/20,
c=S/6.
S(1-1/15-3/20-1/6)=37cm².
Solve for S.
1-(4+9+10)/60=37/60.
S=60.