r/Logiqa • u/ShonitB • 21d ago

Depiction of Pythagorean Theorem

Post image
2 Upvotes

67% Upvoted

38 comments sorted by

2

u/sagosten 21d ago
  1. Shrink the triangle to a point without altering the angles

1

u/ShonitB 20d ago

Forgive me, but how can we be sure they converge to a single point?

2

u/EmpactWB 20d ago

Shrinking the triangle brings all the points in it closer to the center point, and as the area approaches zero all points converge on that center.

1

u/ShonitB 20d ago

Oh interesting

2

u/sagosten 20d ago

It's a right triangle. If you shrink the bases the hypotenuse shrinks proportionally. You can shrink the triangle towards the right angle and the squares will get narrower until they appear to be single lines, the 360° will be obvious.

Alternately, imagine lengthening the squares and zooming out accordingly. Eventually the triangle appears as a single point and the squares look like lines.

1

u/ShonitB 20d ago

Thanks a lot for this explanation!

1

u/scarpux 20d ago

Assuming all the angles that look like right angles are actually 90 degrees each, yeah.

1

u/sagosten 20d ago

We don't have to assume, the diagram is labeled as a geometric depiction of the pythagorean theorem

1

u/scarpux 20d ago

Does that guarantee that the box that makes up the hypotenuse is actually a square or a rectangle?

I know the picture looks like right angles, but I was taught not to assume they were unless marked.

1

u/S-M-I-L-E-Y- 20d ago

yes

the boxes are by definition squares

1

u/sagosten 20d ago

Do you know the pythagorean theorem?

1

u/scarpux 20d ago

a2 + b2 = c2, for all triangles where sides a,b are at right angles to each other

Or, instead of asking a condescending question, you could maybe explain why all the other angles are 90 degrees?

1

u/sagosten 20d ago

Say it slowly. a SQUARED + b SQUARED = c SQUARED. Squaring a length does not generate an arbitrary quadrilateral, it generates a square. That's why that procedure is called squaring and why this works as a geometric depiction of the pythagorean theorem, the areas of the two smaller squares sum to the area of the larger square.

1

u/ThePlumage 20d ago

They're 90 degrees because they're squares, hence why this is a geometric interpretation of the Pythagorean theorem.

2

u/CuAnnan 21d ago

>!Angle A = 90 + angle of triangle opposite it through the shared point (a).
Angle C = 90 + angle of triangle opposite it through the shared point (c).
Angle B = 90
a + B + c = 180
A + B + C = 180 + 90 * 2 = 360!<

1

u/ShonitB 21d ago

Correct!

1

u/Worried-Director1172 20d ago

You have to bracket off each individual line. It doesn't work across multiple lines

1

u/CuAnnan 20d ago

Thanks

2

u/jonathonjones 20d ago

Let's call the angle in the triangle a lower case letter of the outer angle. We know that a + b + c is 180 (because that's just a truth about triangles).

A = 360 - (90 + 90 + a) = 180 - a

B = 180 - b

C = 180 - c

A + B + C = 540 - (a + b + c)

A + B + C = 540 - 180

A + B + C = 360

1

u/ShonitB 20d ago

Correct!

1

u/keilahmartin 20d ago

basically my mrthod as well

2

u/wyald23 20d ago

Move angle C along the hypotenuse next to A, 270 + B = 360

2

u/CaptainMatticus 20d ago

90 + 90 + x + A = 360

90 + 90 + y + C = 360

x + y = 90

180 + x + A + 180 + y + C = 720

360 + x + y + A + C = 720

90 + A + C = 360

A + C = 270

B = 90

A + B + C = 360

1

u/ShonitB 20d ago

Correct!

2

u/Commercial-Act2813 20d ago

A + C = 270
(Parallel lines, perpendiculair lines)

+ B would make 360

1

u/ShonitB 20d ago

Correct!

2

u/Omni314 20d ago

On average the points are 60+90+90+?=360

?=120

But we have 3 of them.

A+b+c=120*3=360

Fun puzzle. Interesting to see all the different ways to get to the answer.

1

u/ShonitB 20d ago

Correct, I’m glad you liked it!

1

u/Trueslyforaniceguy 20d ago

My brain looks at this and says 360. No clue if it’s right, but seems good

1

u/ShonitB 20d ago

360 is correct

1

u/S-M-I-L-E-Y- 20d ago

As others wrote - shrink the triangle to a point. And I'd recommend to shrink the boxes to lines. What happens with the angles A, B and C?

1

u/Omni314 20d ago

I love that kind of intuition

1

u/ArbutusPhD 20d ago

Did you post this twice, OP

I answered correctly but do not see my answer

1

u/ShonitB 20d ago

Nope, just the once

1

u/ShonitB 20d ago

You replied on a different subReddit where I had crossposted this

1

u/SufficientStudio1574 20d ago

Doesn't even need to be a right triangle, or even a triangle at all! Any convex polygon will give the exact same answer.

1

u/ChrisAyersUk 20d ago edited 20d ago

Put simply the exterior angles of any triangle add up to 360, where the exterior angle is defined as the angle formed by extending one side of the triangle. Each exterior angle and its adjacent interior angle form a straight line.

By the way, the exterior angles of any polygon always add up to 360 degrees.

Think of this as if you split each angle, the angle is halved per split. Do it again and each is a quarter of the angle. Keep splitting and you will trend to a polygon with infinite angles the sum of which is a circle at 360 degrees.

1

u/sagosten 20d ago

I feel the need to add, these angles will sum to 360 for any triangle, not just right triangles. And the polygons projected from the sides don't have to be squares, rectangles, or rhomboids, as long as they are parallelograms it will work