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congruency

congruency (ˈkɒŋgruːənsɪ) [f. as prec.: see -ency.] 1. The quality or state of being congruent; congruity. of a congruency: see prec. 2 b.1494 Fabyan Chron. vii. 370 They agreed to reste there styll, and that of a congruency, for they myght dwell in no lande where they shulde more suerly be defended... Oxford English Dictionary

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Phase congruency

Foundations Phase congruency reflects the behaviour of the image in the frequency domain. The method of phase congruency applies to many cases where other methods fail. wikipedia.org

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Congruency in bow-tie triangles We've just started congruency in my class, and we've stumbled across a question which goes like this: !Diagram 1 > Prove that ∆AOB $\equiv$ ∆COD I drew up a diagram which portrays ex...

I would assume that they are straight lines, because, as you said, it is false if you assume otherwise. However, usually some text describing the construction of the figure is nearby, and it would tell you something like "Let O be the intersection of lines AD and BC".

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Congruency and eigen values $If$ $two$ $matrices$ $are$ $congruent$ $then$ $they$ $have$ $the$ $same$ $eigen$ $values$ $??$ I have tried solving it using definition of congruent matrices taking eigen value but didn't...

It is wrong $\pmatrix{0&1\cr1&0\cr}$ and $\pmatrix{2&1\cr0&-1/2\cr}$ are congruent but the first one has $1$ and $-1$ as eigen values and the second one has $2$ and $-1/2$ as eigen values.

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Quadrilateral congruency theorem Is there a congruence theorem that says that if three sides of two quadrilaterals are equal, then the two quadrilaterals are congruent? I am grading some homework and a student appeal...

I'm sorry, but the student is out of luck. No there isn't such a theorem, and for good reason. Indeed, if all four sides of a quadrilateral are equal in length to the sides of another quadrilateral, _even then_ we cannot conclude the quads are congruent. A simple counter-example suffices: > Consider...

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Congruency of Numbers: Last digit of $(1234)^{64} + 3,333,333,333,333$ What is a single digit number that is congruent to (1234)$^{64}$ + 3,333,333,333,333 (mod 10)? Show all work.

HINTS: We can immediately reduce this problem to $(1234)^{64} + 3 \mod 10$ (Can you explain why?) Then the problem is really to reduce $(1234)^{64} \mod 10$. But this is actually just $4^{64}\mod 10$. Can you see why this one happens? Can you finish from here?

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Solving Congruency Using Quadratic Reciprocity Use quadratic reciprocity to show that if p is an odd prime different from 5, then 5 is a quadratic residue (mod p) if and only if p $\equiv\pm$ 1 (mod 5).

Applying the Quadratic Reciprocity law in your example we know that for $5$ to be a quadratic residue $\mod p$ and $p\ne 5$ the following conditions must satisfy: The legendre symbol $(\frac{p}{5})$ and $(\frac{5}{p})$ are both equal, which means that 5 is a quadratic residue modulo every odd prime ...

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How to calculate this congruency? Let's say I have this linear congruency: $2x + 1234 = 7 \mod 17$. Without "$+1234$" I would've used the following formulas: $x = x_0 + k(\dfrac{m}{gcd(a, m)})$, whereas $ax_0 + my_0 =...

I would calculate everything mod. $17$: $\;1234\equiv 10\mod 17$, so the equation becomes $$2x+10\equiv 7\mod17\iff 2x\equiv-3\equiv14\mod 17. $$ Now as $2$ is a unit mod. $17$, we may apply the _cancellation law_ : $$2x\equiv 14=2\cdot 7\mod17\iff x\equiv 7\mod 17.$$

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Proving the congruency of triangles How can I prove the congruency? I have tried, $\angle{CDA}=\angle{DCB}$ But, which rule should I use? !enter image description here

HINT : The quadrilateral $ABCD$ is a parallelogram.

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What is the difference between congruency and equality? What is the difference between equality and congruency? When should I say that two figures are congruent and when that they are equal?

In geometry, a "figure" is a set of points in the plane. So, two figures are _equal_ if they have the same points. In other words, two equal figures are exactly equal: the same figure. Congruent figures have the same shape and size (informally) but possibly different points. No diagram is needed for...

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Prove this modular congruency? Prove that $2^{2x} \equiv 1 \mod 3$ for any integer $x$?. I know this is true but is there a nice way to prove it?

**HINT:-** An approach which does not involve modular arithmetic. R.T.P. $2^{2x} \equiv 1 \mod 3$ or,$2^{2x}-1$ is divisible by $3$. Now,$2^{2x}=4^x$ So,prove by induction now that $4^x-1$ is divisible by $3.$.'

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Confusion over SSA axiom for congruency I was browsing through KHAN Academy videos when I met the one which Explained why SSA is not a Congruency postutate. But I had this Diagram in my Mind(Different from the video) ...

No, it is not. See SSA > "Side-Side-Angle condition: If two sides and a corresponding non-included angle of a triangle have the same length and measure, respectively, as those in another triangle, then this is not sufficient to prove congruence; but if the angle given is opposite to the longer side ...

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How do I solve this congruency? I have this congruence relation: 2013 ≡ 1012 (mod m) I am supposed to find all m in the natural system.

$2013\equiv 1012\pmod m\implies m|(2013-1012)\implies m|1001$. Thus all factors of $1001$ satisfy this.

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Is it possible to solve this congruency system? I need help to determine if this congruency system can be solved and if it can be solved how do I do it: $$\begin{cases}x\equiv2\text{ (mod $3$)}\\\ x\equiv4\text{ (mod ...

$$x=6k+4\implies x=3(2k+1)+1$$ Thus if $$x\equiv 4\pmod {6} $$ then $$x\equiv 1\pmod 3$$ That is the system $$\begin{cases} x\equiv 2 \pmod{3} \\\ x\equiv 4 \pmod{6} \end{cases}$$ is not consistent.

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Number of equivalence classes regarding congruency of symmetric bilinear forms Let $n \in \mathbb{N}$. Let $V$ be a $n$-dimensional vector space over a field $K$. Consider the set of symmetrical bilinear forms over...

Translating this to a less abstract language. If $n$ is finite the set of symmetric forms corresponds to the set of $n\times n$ symmetric matrices. Two symmetric forms are equivalent if there is a basis that makes the two congruent. There exists a $P$ such that $A = P^{-1} B P$ And since all symmetr...

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congruency

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congruency

Phase congruency

Congruency in bow-tie triangles We've just started congruency in my class, and we've stumbled across a question which goes like this: !Diagram 1 > Prove that ∆AOB $\equiv$ ∆COD I drew up a diagram which portrays ex...

Congruency and eigen values $If$ $two$ $matrices$ $are$ $congruent$ $then$ $they$ $have$ $the$ $same$ $eigen$ $values$ $??$ I have tried solving it using definition of congruent matrices taking eigen value but didn't...

Quadrilateral congruency theorem Is there a congruence theorem that says that if three sides of two quadrilaterals are equal, then the two quadrilaterals are congruent? I am grading some homework and a student appeal...

Congruency of Numbers: Last digit of $(1234)^{64} + 3,333,333,333,333$ What is a single digit number that is congruent to (1234)$^{64}$ + 3,333,333,333,333 (mod 10)? Show all work.

Solving Congruency Using Quadratic Reciprocity Use quadratic reciprocity to show that if p is an odd prime different from 5, then 5 is a quadratic residue (mod p) if and only if p $\equiv\pm$ 1 (mod 5).

How to calculate this congruency? Let's say I have this linear congruency: $2x + 1234 = 7 \mod 17$. Without "$+1234$" I would've used the following formulas: $x = x_0 + k(\dfrac{m}{gcd(a, m)})$, whereas $ax_0 + my_0 =...

Proving the congruency of triangles How can I prove the congruency? I have tried, $\angle{CDA}=\angle{DCB}$ But, which rule should I use? !enter image description here

What is the difference between congruency and equality? What is the difference between equality and congruency? When should I say that two figures are congruent and when that they are equal?

Prove this modular congruency? Prove that $2^{2x} \equiv 1 \mod 3$ for any integer $x$?. I know this is true but is there a nice way to prove it?

Confusion over SSA axiom for congruency I was browsing through KHAN Academy videos when I met the one which Explained why SSA is not a Congruency postutate. But I had this Diagram in my Mind(Different from the video) ...

How do I solve this congruency? I have this congruence relation: 2013 ≡ 1012 (mod m) I am supposed to find all m in the natural system.

Is it possible to solve this congruency system? I need help to determine if this congruency system can be solved and if it can be solved how do I do it: $$\begin{cases}x\equiv2\text{ (mod $3$)}\\\ x\equiv4\text{ (mod ...

Number of equivalence classes regarding congruency of symmetric bilinear forms Let $n \in \mathbb{N}$. Let $V$ be a $n$-dimensional vector space over a field $K$. Consider the set of symmetrical bilinear forms over...