Deducing the Pythagorean Theorem from a particular dissection How can I

Audrina Jackson 2022-07-01 Answered
Deducing the Pythagorean Theorem from a particular dissection

How can I deduce the pythagorean theorem from the follow image?
I have been draw some parallels and I got the figure but I don't know how to deduct, some hint?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Answered 2022-07-02 Author has 17 answers
Note that each colored piece in the big square with side length c appears once in the small squares with side lengths a and b. From this, the sum of the areas of the small squares is equal to the area of the big square, or a 2 + b 2 = c 2

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-07-06
The Pythagorean theorem and Hilbert axioms
Can one state and prove the Pythagorean theorem using Hilbert's axioms of geometry, without any reference to arithmetic?
Edit: Here is a possible motivation for this question (and in particular for the "state" part of this question). It is known that the theory of Euclidean geometry is complete. Every true statement in this theory is provable.
On the other hand, it is known that the axioms of (Peano) arithmetic cannot be proven to be consistent. So, basically, I ask if there is a reasonable theory which is known to be consistent and complete, and in which the Pythagorean theorem can be stated and proved.
In summary, I guess I am asking - can we be sure that the Pythagorean theorem is true? :)
asked 2022-06-22
Pythagorean theorem
We can make a square into four equal squares. Fine, if we want to make into five.. Then there is a problem. Please discuss, How to make five squares from a single square by using a Pythagorean theorem. Is there any other way to make five squares from one square without using Pythagorean theorem? Please discuss. Thanking you, KKRG
asked 2022-05-09
Triangle law of vector addition vs Pythagorean theorem
Suppose there is a vector a of magnitude 5 units to the east, another vector b of magnitude 6 units to the north. To find magnitude of vector a + vector b,
By the triangle law of vector addition, it is 5 + 6 units = 11 units.
By Pythagorean theorem, it is ( 5 2 + 6 2 ) = ( 61 )
Which answer is right? If so, why is the other wrong?
Thank you!
asked 2022-09-12
The legs of a right triangle are 6 and 8 cm. Find the hypotenuse and the area of ​​the triangle.
asked 2022-06-20
Pythagorean Theorem intuition
I actually have a degree in Pure Mathematics, and this has always bugged me. Like a tiny, hardly-noticeable stone in your shoe you just can't get out.
Despite being at the core of geometry, arithmetic, and infinity, despite being able to prove it a dozen different ways, and despite it being the first "formula" anyone learns and one of the oldest known mathematical ideas - I can only see shadows and silhouettes of its truth.
Looked at from the point of view of geometry, I can see the statement plainly as a statement regarding the intrinsic notions of angle and area (using the proof of similar right-angle triangles) - however, the last step requires a correspondence between the notions of length and area to make complete (namely, the area of a shape increases quadratically as its scale increases linearly). This has always bothered me, since, the Theorem is an idea solely between angle and length.
There are, of course, simple proofs that don't depend on the notion of area (ex: Pythagorean Theorem Proof Without Words 6), however, sadly, they don't further my intuition, despite being clever/cute.
Staring at the statement blank in the face, I understand it far less intuitively then I do half of the ideas in algebra, analysis, number theory, etc.
asked 2022-06-17
Approximation using pythagorean theorem
Im looking at the following diagram,

Here, I am interested in a relation between a,s,c, assuming that r >> 1 my first thought is to relate then using the pythagorean theorem,
c 2 = a 2 + s 2
Is making sure an approximation a good approach and is there an alternate way to relate my variables? Thank you in advance!
asked 2022-07-27
A 10-m ladder is leaning against a building. The bottom of theladder is 5-m from the building. How high is the top of theladder?

New questions