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# What is a conjecture in geometry

### Conjecture (Geometry, Proof) - Mathplane

1. A conjecture is an educated guess that is based on known information
2. The precise statement of the conjecture is: Conjecture (Tangent Conjecture I): Any tangent line to a circle is perpendicular to the radius drawn to the point of tangency.Conjecture (Tangent Conjecture II): Tangent segments to a circle from a point outside the circle are equal in length
3. The first conjecture might seem to some to be the definition of a rectangle - a polygon with four 90 degree angles - but the actual definition we are using is as follows: A rectangleis defined to be an equiangular parallelogram
4. Formally, a conjecture is a statement believed to be true based on observations. In general, a conjecture is like your opinion about something that you notice or even an educated guess. Looking at..

Definition Of Conjecture. Conjecture is a statement that is believed to be true but not yet proved. Examples of Conjecture. The statement Sum of the measures of the interior angles in any triangle is 180° is a conjecture. Here is another such conjecture: If two parallel lines are cut by a transversal, the corresponding angles are congruent In math, the term conjecture refers to a specific statement that is thought to be true but has not been proven. In geometry, there are many different conjectures, such as the sum of angles in a triangle, linear pair, parallel lines and inscribed angle conjectures

### Conjectures in Geometry: Tangen

A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. Conjectures must be proved for the mathematical observation to be fully accepted. When a conjecture is rigorously proved, it becomes a theorem In mathematics, Thurston's geometrization conjecture states that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with it Conjecture definition is - inference formed without proof or sufficient evidence. How to use conjecture in a sentence. Did you know

### Conjectures in Geometry: Rectangle Conjecture

1. A conjecture is a good guess or an idea about a pattern. For example, make a conjecture about the next number in the pattern 2,6,11,15 The terms increase by 4, then 5, and then 6. Conjecture: the next term will increase by 7, so it will be 17+7=24. What is the meaning of conjecture in maths
2. A conjecture is an educated guess. Sometimes it may be true, and other times it may be false. How do you know whether a conjecture is true or false? Try out different examples to test the conjecture. If you find one example that does not follow the conjecture, then the conjecture is false. Such a false example is called a counterexample
3. A conjecture is some sort of mathematical statement that is formed with incomplete knowledge. In other words, it's a guess— mathematicians form conjectures and then try to prove them either true or false. They're a lot like hypotheses

### Conjecture in Math: Definition & Example - Video & Lesson

1. A conjecture is an educated guess that is based on examples in a pattern. A counterexample is an example that disproves a conjecture. Suppose you were given a mathematical pattern like h = \begin {align*}-16/t^2\end {align*}. What if you wanted to make an educated guess, or conjecture, about h
2. The Goldbach conjecture, dating from 1742, says that the answer is yes. Some simple examples: 4=2+2, 6=3+3, 8=3+5, 10=3+7, , 100=53+47, . What is known so far: Schnirelmann (1930): There is some N such that every number from some point onwards can be written as the sum of at most N primes. Vinogradov (1937): Every odd number from some.
3. Math 11 Foundations: Unit 8 - Logic & Geometry Sardis Secondary Foundationsmath11.weebly.com Mr. Sutcliffe Example 1: Make a conjecture about intersecting lines and the angles formed. Example 2: Use inductive reasoning to make a conjecture about the product of an odd integer and an even integer. Example 3: Make a conjecture about the sum of two odd numbers

### Definition of Conjecture Define Conjecture - Free Math

1. ary supporting evidence, but for which no proof or disproof has yet been found. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of.
2. Conjecture 1 (Tate) Suppose is finitely generated over its prime field. () The map ( 2) is bijective. () The -adically homological equivalence is the same as the numerical equivalence on . In particular, does not depend on the choice of . Remark 1 Finitely generated fields are of arithmetic nature: finite fields and global fields are finitely.
3. What is Conjecture Conjecture is a theory based on evidence with only a slight degree of credibility. It is an idea of fact, or potential cause or occurrence, as suggested by another fact, which is too feeble to prove the idea. A conjecture is even less substantial than a hypothesis, which is generally based on well-accepted facts

### What Does Conjecture Mean in Math? - Reference

1. chapter 6 geometry conjectures and numerous books collections from fictions to scientific research in any way. in the middle of them is this chapter 6 geometry conjectures that can be your partner. Since Centsless Books tracks free ebooks available on Amazon, there may be times when there is Chapter 6 Geometry Conjectures - fa.quist.c
2. What is conjecture give an example for it in geometry? Conjecture is a statement that is believed to be true but not yet proved. Example: 1) The statement Sum of the measures of the interior angles in any triangle is 180° is a conjecture. 2) If two parallel lines are cut by a transversal, the corresponding angles are congruent..
3. g a proof of this conjecture (the proof soon was found to have a flaw).One change over the last five years is that now there are excellent.
4. But a good conjecture will guide math forward, pointing the way into the mathematical unknown. A conjecture creates a summit to be scaled, a potential vista from which mathematicians can see entirely new mathematical worlds. Mountain climbing is a beloved metaphor for mathematical research. The comparison is almost inevitable: The frozen world.
5. This also proves there are 0 2-sided shapes with sides that enclose 2 angles if the conjecture is true, but it is not undefined. In contrast, the number of 1-sided shapes with sides that enclose 1 angle is probably undefined (another conjecture)
6. Conjecture geometry is a very useful tool. A conjecture is a hypothesis. Some of the hypothesis is when 2 angles form a linear pair the addition of the angles is 180 degrees. The vertical angle conjecture is when 2 angles are vertical angles, and then both measure the same or are congruent. This way there are differen

Start studying Geometry: Conjectures Set 1. Learn vocabulary, terms, and more with flashcards, games, and other study tools Once a conjecture is posed, ask the class what they need to do to understand it and begin to develop an outline that all can use. Regular opportunities for practice with the different skills (organizing data, writing conjectures, etc.) will lead to greater student sophistication over time Throughout Geometry, students write definitions and test conjectures using counterexamples. When writing definitions, counterexamples are useful because they ensure a complete and unique description of a term. If a counterexample does not exist for a conjecture (an if - then statement), then the conjecture is true

Scientists solve 90-year-old geometry problem. John Mackey, left, and Marijn Heule have pursued a math puzzle known as Keller's conjecture for decades. They found a solution by translating it into. Explanation: The arc length of a circle is the distance from one point on the circumference to another point on the circumference, traveling along the edge of the circle. Because we know that the measure of the central angle is equal to the arc it intercepts, (Inscribed angle conjectures) by dividing that measure by 360 degrees, we find out what fraction of the circumference that the arc covers Conjecture : Conjecture is a statement or conclusion drawn from what we know, without having any proper proof. It is believed to be true based on an incomplete information and observation. Conjecture is nothing but a hypothesis or an initial conclusion to a scientist. Riemann hypothesis and Fermat's Last Theorem are the two major conjecture. The conclusion you draw from inductive reasoning is called the conjecture. A conjecture is not supported by truth. When making a conjecture, it is possible to make a statement that is not always true. Any statement that disproves a conjecture is a counterexample. Examples: 1. Determine the number of points in the 4th, 5th, and 8th figure. 2

Conjecture: A statement believed to be true, but for which we have no proof. (a statement that is beingproposedto be a true statement). Axiom: A basic assumption about a mathematical situation. (a statement we assume to be true). Examples De nition 6.1: A statement is a sentence that is either true or false{but not both. ([H], Page 53) A conjecture is a suggestion of a possible theorem which has not yet been proven. In 1969, Milnor stated a conjecture about spaces with positive Ricci curvature. He conjectured that such a space can only have finitely many holes. I am working on trying to find a proof for this conjecture and so are many other Riemannian Geometers conjectures 1 NAEP 2005 Strand: Geometry Topic: Mathematical Reasoning Local Standards: _____ Lesson 1-1 Patterns and Inductive Reasoning reasoning based on patterns you observe. conjecture an example for which the conjecture is incorrect. half 224 12 2 2 Thursday 29 37 Friday Geometry Lesson 1-2 Daily Notetaking Guide L1 conjecture for quadrics [JP15] and given a new proof of the Gieseker-Petri theorem [JP14]. Cartwright [C13] has introduced abstract tropical complexes which, in the two-dimensional case [C13], have a rich theory mirroring that of algebraic surfaces

### Conjectures Brilliant Math & Science Wik

• Collatz Conjecture Calculato
• Geometry Conjectures. STUDY. Flashcards. Learn. Write. Spell. Test. PLAY. Match. Gravity. Created by. Mitchell1. Terms in this set (35) Linear Pair Conjecture. If two angles form a linear pair then the measures of the angles add up to 180°. Vertical Angles Conjecture
• In a legal sense, the term conjecture refers to guesswork, meaning it is a supposition based on theory or opinion, without substantial evidence. Conjectures are often based on the way a situation appears, rather than on solid proof. For instance, the media often makes conjectures about the state of celebrities' marriages based on rumor and photos submitted by unsubstantiated sources
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• Complete the conjecture based on the patterns you observe:Conjecture: The product of a number n-1 and the number n+1 is always equal to _____. Strategies for Differentiation Have students use presentation software to create presentations of the vocabulary terms
• Y. Hoshi (a student of Mochizuki) proved that an analogous generalization of the section conjecture is false: Existence of nongeometric pro-p Galois sections of hyperbolic curves, Publications of the Research Institute for Mathematical Sciences (Publ. Res. Inst. Math. Sci.) 46 (2010), no. 4, 829-848

### FAQ: What Is A Conjecture In Math? - Math lessons and problem

Basically, Hodge conjecture connects the algebraic cycles, an object in algebraic geometry, with some type of component of cohomology group, an algebraic topological information. There are several versions of Hodge conjecture. In fact, the original one was proven to be false, and it has been modified and generalized in a way that it is. Finally, the ABC-Conjecture is just a piece of a much larger framework in the field of Arithmetic Geometry which, roughly, tries to create a framework where geometry and arithmetic become indistinguishable and where you can use methods of one to solve problems in the other Chapter 7 Geometry Conjectures - pompahydrauliczna.eu Chapter 7 Geometry Conjectures Getting the books chapter 7 geometry conjectures now is not type of inspiring means. You could not lonely going subsequent to book deposit or library or borrowing from your links to right of entry them. This is an totally easy means to specifically get lead by. The converse of Conjecture 1a is also true: Conjecture 1b: If a line is drawn from the centre of a circle to the midpoint of a chord, then the line is perpendicular to the chord. We can use these conjectures about the relationship between the line and the chord to solve problems. Available on website: school-maths.co

### Geometrization conjecture - Wikipedi

Create & Prove Conjecture - Discrete Math (Proofs) Imagine that a building has been overrun with snakes and rats. To help curb the problem, the building manager decides to offer employees brownie points for capturing and relocating them. They offer 13 points for each snake and 6 points for each rat captured and removed This chapter 6 geometry conjectures, as one of the most involved sellers here will unquestionably be in the middle of the best options to review. Wikibooks is a useful resource if you're curious about a subject, but you couldn't reference it in academic work counterexample definition conjecture. A key term in geometry is counterexample. the way we define counterexample is an example that makes a definition or conjecture incorrect. The reason why this is important is because if you can find a counterexample for a definition, let's say a teacher asks you to write the definition of a rectangle  Conjecture is a synonym of theorem. As nouns the difference between conjecture and theorem is that conjecture is (formal) a statement or an idea which is unproven, but is thought to be true; a while theorem is (mathematics) a mathematical statement of some importance that has been proven to be true minor theorems are often called propositions'' theorems which are not very interesting in. Conjecture definition, the formation or expression of an opinion or theory without sufficient evidence for proof. See more It was conjectured that this fact would hold in general, and it came to be known as the bellows conjecture. In the period from 1995-1997, Idjad Sabitov proved the bellows conjecture by showing that for any (oriented) polyhedron P, the volume of P is a root of a polynomial depending only on the combinatorial structure and edge lengths of P conjecture meaning: 1. a guess about something based on how it seems and not on proof: 2. to guess, based on the. Learn more Conjectures and Counterexamples. A conjecture is an educated guess that is based on examples in a pattern. Numerous examples may make you believe a conjecture. However, no number of examples can actually prove a conjecture. It is always possible that the next example would show that the conjecture is false

The Collatz Conjecture (also known as the 3 n + 1 problem, the Ulam conjecture, or the Hailstone problem) was introduced by Lothar Collatz in 1939. The conjecture starts with a process: Choose any number. If it is even, divide it by 2. If it is odd, multiply it by 3 and then add 1. Repeat with the new number. The conjecture states no matter. Chapter 12: Euclidean geometry. This chapter focuses on solving problems in Euclidean geometry and proving riders. It must be explained that a single counter example can disprove a conjecture but numerous specific examples supporting a conjecture do not constitute a general proof A conjecture is the formation of an opinion that is based on incomplete information. However, I may be wrong Goldbach Conjecture : Goldbach Conjecture is one of the oldest, unresolved and best known conjecture used in mathematics, particularly in number theory. The conjecture states that, Every even integer greater than 2 can be expressed as the sum of two primes. This conjecture is shown true for even numbers upto 4 x 10 18 A simply connected manifold. In two dimensions, the Conjectures says that a blob, a bun or a pancake are all homeomorphic to a sphere, which is a basic result of topology

### Conjecture Definition of Conjecture by Merriam-Webste

• Poincaré Conjecture. If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then.
• GEOMETRY SEM 2 APEX GEOMETRY S. The Students' Conjectures: The students are running a pony ride business. Complete the table below to summarize what you know about each student's conjecture: (, 1 point for each row of the chart) Math Geometry GEOMETRY SEM 2 APEX GEOMETRY S. Comments (5) 9.3.5 Journal: Point on a Circle
• Conjecture. Conjecture - Displaying top 8 worksheets found for this concept.. Some of the worksheets for this concept are Dg3tw593 71602 730 pm 122 conjectures, Geometry name chapter 2 work, Give a counterexample that disproves each conjecture, Conjectures, Examples patterns and conjectures, Unit 4 logic packet, Geometry chapter 2 reasoning and proof, 2 1 patterns and inductive reasoning.

### What Is Conjecture In Math? - Math lessons and problem

analogue of Conjecture 1.2, that u ([DV]) 2 K0(Bˇ) is a birational invariant of V. This fact is somewhat stronger than Conjecture 1.2, since it implies the latter but also gives some torsion information. And nally, Borisov and Libgober  have now proven an analogue of Conjecture 1.2 with the Todd genus replaced by th standing what math is and what a mathematician does: Mathematicians seek out patterns and use them to formulate new conjectures. Mathemati-cians resolve the truth or falsity of conjectures by mathematical proof. For an illustration of this, let's go back to Euclidean geometry and the angles of a triangle, as in Figure 1 Recently Kewei Zhang provided a new proof of the uniform Yau--Tian--Donaldson conjecture for Fano manifolds, a central problem in Kähler geometry which was resolved (at least in the same generality as Zhang's new proof) in 2012 by Chen--Donaldson--Sun 6.A counterexample _____. is a proof that is not valid cannot be used to prove or disprove a conjecture shows that a conjecture is always true shows that a conjecture is not always true 7. Using the diagram below as reference, write a paragraph proof to prove that the symmetric property of congruence exists for any two angles. Given: ∠ A is congruent to ∠ Prove: ∠ B is congruent to ∠. Discovering Geometry Practice Your Skills CHAPTER 4 27 Lesson 4.4 • Are There Congruence Shortcuts? Name Period Date In Exercises 1-3, name the conjecture that leads to each congruence. 1. PAT IMT 2. SID JAN 3. TS bisects MA ,MT AT , and MST AST In Exercises 4-9, name a triangle congruent to the given triangle and state the congruence.

conjecture. Opposite of an opinion or conclusion formed on the basis of incomplete information. Opposite of a thing that is accepted as true or as certain to happen, without proof. You can't escape the fact that mass tourism is ruining the very things it wants to celebrate. conjecture ( countable and uncountable, plural conjectures) (formal) A statement or an idea which is unproven, but is thought to be true; a guess. I explained it, but it is pure conjecture whether he understood, or not. (formal) A supposition based upon incomplete evidence; a hypothesis Math(PleaseHelp!) Consider the following conjecture: the sum of two even numbers will be even. A.) give three examples supporting the conjecture. (I gave 2+2=4 4+4=8 10+10=20) B.) Prove the conjecture( this is the part I need help with) Multiple Choice HELP! What is a counterexample for the conjecture Access Free Chapter 9 Project Proving A Conjecture Answers Chapter 9 project proving a conjecture answers 9 Credibility of Qualitative Studies CHAPTER ˜e Medieval alchemi-cal symbol for ﬁre was a single triangle, also the modern symbol for tri-angulation in geometry, trigonometry, and survey - ing: the process of locat-ing a Conjectures play a very important role in problem-solving in Mathematics and Geometry, where the solution is not always apparent and we generate the solution by following a series of steps. Generally, each of these steps is a 'Conjecture' over the previous step

• 1. Students will discover the eight conjectures covered in background knowledge. Materials: Geometry software Worksheets Procedures: Each of these conjectures is covered as a separate problem in the lab that follows. The student should be able to discover these conjectures themselves by working out the problems using Cabri
• The Hopf sign conjecture from the 1930ies is an important open problem in the eld of global Riemannian geometry, where local quantities like curvature are linked to global quantities like Euler characteristic. It is motivated rst of all from the case d= 1 where it follows from Gauss-Bonnet. The sign is explained that products M
• ute elementary introduction to the Birch and Swinnerton-Dyer conjecture presented at the farewell party for Chen-Yu Chi, who was leaving Harvard after his 8 years as a graduate student and a junior fellow here. As majority of the audience are in.
• Conjectures 1, 4, and 7 have two similar statements. Only difference is the order of the numbers is reversed. Once one conjecture is established the other follows from it. Conjectures in table are related in interesting and important ways. Parallels between addition and subtraction of zero and multiplication and division by on
• ant of our senses) to remember theorems, understand proof, inspire conjecture, perceive reality, and giv
• To show that a conjecture is false, you have to find only one example in which the conjecture is not true. This case is called a counterexample . A counterexample can be a drawing, a statement, or a number. Inductive Reasoning 1. Look for a pattern 2. Make a conjecture. 3. Prove the conjecture or find a counterexample

### What is a conjecture in math? - Quor

Definition of conjecture in the Definitions.net dictionary. Meaning of conjecture. What does conjecture mean? Information and translations of conjecture in the most comprehensive dictionary definitions resource on the web For Exercises 13-15, use inductive reasoning to test each conjecture. Decide if the conjecture seems true or false. If it seems false, give a counterexample. 13. Every odd whole number can be written as the difference of two squares. 14. Every whole number greater than 1 can be written as the sum of two prime numbers. 15

Abstract. In 1980, Gross conjectured a formula for the expected leading term at s = 0 of the Deligne-Ribet p -adic L -function associated to a totally even character ψ of a totally real field F. The conjecture states that after scaling by L ( ψ ω − 1, 0), this value is equal to a p -adic regulator of units in the abelian extension of F. Abstract: After a Hessian computation, we quickly prove the 3D simplex mean width conjecture using classical methods. Then, we generalize some components to dimensions. Comments: Subjects: Metric Geometry (math.MG); Information Theory (cs.IT) MSC classes: 52-02. Cite as Conjecture: The sum of opposite angles of a quadrilateral inscribed in a circle is 180°. Proof: Take a closer look at the angles around the center of the circle, and then use the theorem about inscribed and central angles Jill looked at the following sequence 0 3 8 15 24 35 and it just keeps going I guess with the dot dot dot she saw that the numbers were each one less than a square number 0 is 1 less than 1 which is a square number 3 is 1 less than 4 8 is 1 less than 9 15 is 1 less than 16 yeah they're all 1 less than a square number and conjectured that the nth number would be N squared minus 1 now conjecture. Argument: If a number is divisible by 2, then it is even. The number 4 is divisible by 2. Therefore, the number 4 is even. A conjecture and the flowchart proof used to prove the conjecture are shown

### Conjectures and Counterexamples ( Read ) Geometry CK

The Collatz Conjecture is one of the most easily stated, yet notoriously hard unsolved problems in Number Theory. First, I will attempt to present an abridged version of the history, heuristics, and computations behind the conjecture. This will be followed by discussions of some recent (and not so recent) advances on this conjecture. If time. 5. Goldbach's Conjecture. Equation: Prove that x + y = n. where x and y are any two primes. n is ≥ 4. This problem, as relatively simple as it sounds has never been solved. Solving this problem will earn you a free million dollars. This equation was first proposed by Goldbach hence the name Goldbach's Conjecture The Sato-Tate Conjecture is a statement about the statistical distribution of certain sequences of numbers. As an example, consider the following formal product in the variable q: If we multiply everything out, we get a formal power series: The coefficient of q n in this power series is traditionally called τ (n), and the function that maps n. 1-Factorization Conjecture (if G is a 2m-vertex regular graph with degree at least 2⌈m/2⌉-1, then G is 1-factorable --- implied by Overfull Conjecture) Total Coloring Conjecture (the vertices and edges of a graph G can be colored with Δ(G)+2 colors such that adjacent vertices have different colors, incident edges have different colors, and.

On the calculation of local terms in the Lefschetz-Verdier trace formula and its application to a conjecture of Deligne, Ann. of Math. 135, 483-525 (1992) Article MathSciNet Google Scholar. Raynaud, M.: Géométrie analytic rigide, d'après Tate, Kiehl, Bull. Soc. Math. France Mémoir 39-40. 319-327 (1974 Using the Collatz Conjecture, show how we get to oneness from 27 We start with n = 27 Step 1 → n = 27 Since 27 is odd, we take 3(27) + 1 → 81 + 1 = 82 Step 2 → n = 82 Since 82 is even, we divide by 2 to get 82 ÷ 2 = 41 Step 3 → n = 41 Since 41 is odd, we take 3(41) + 1 → 123 + 1 = 124 Step 4 → n = 12 The first 50 even numbers written as the sum of two primes. Credit: A. Cunningham via WikiCommons, CC-BY SA 3.0. To date, the Goldbach conjecture has been verified for all even integers up to 4 × 10 18 but an analytic proof still eludes mathematician. Although mathematicians do not have a rigorous proof yet, the general consensus is that the conjecture is true Download Free Discovering Geometry Chapter 9 Conjectures Discovering Geometry Chapter 9 Conjectures If you ally craving such a referred discovering geometry chapter 9 conjectures books that will manage to pay for you worth, get the categorically best seller from us currently from several preferred authors

### Goldbach's Conjecture - Math Fun Fact

• Guesswork and conjectures. Formulate and write down questions and conjectures. When we make a guess in mathematics, we usually call it a conjecture. Examples. Constructing appropriate examples is extremely important. Exploration often requires looking at lots of examples
• Conjecture: 1/(7n) will always have the same 6 digits repeating in some order. Not only is the focus on questions and conjecture much more alive than math, students who have this kind of experience will retain a much deeper and robust understanding of what's actually true
• By borrowing a half from each and combining, it is natural to inquire whether, and perhaps even conjecture that, A quadrilateral with a pair of equal opposite sides and a pair of equal opposite angles is a parallelogram. Patrick's construction serves a counterexample to this conjecture
• A conditional statement can be expressed as If A, then B. A is the hypothesis and B is the conclusion. A counterexample is an example in which the hypothesis is true, but the conclusion is false. If you can find a counterexample to a conditional statement, then that conditional statement is false
• Millennium Prize Problems. In 2000, the Clay Mathematics Institute of Cambridge, Mass., identified seven math problems it deemed the most important classic questions that have resisted solution over the years
• All of those reasoning math practices that are difficult to get in kind of fall together when you have them work on conjectures. Teacher: I want you to try to make a conjecture. So the end goal is to kind of analyze this whole set of functions and think about is there a conjecture you can make
• Scientists recently announced progress on an elusive problem from 1960 known as the Sunflower Conjecture.While it doesn't involve any plant biology, it does deal with objects called.

### Conjecture - Wikipedi

A famous conjecture of Alon stated that for fixed d, random d-regular graphs on a large number of vertices have almost optimal spectral gap between the two largest eigenvalues of the adjacency operator. Friedman proved this conjecture in 2008. Friedman also broadened the conjecture to random large-degree covering spaces of a fixed finite base. Geometry. Find one counterexample to show that each conjecture is false. The product of two positive numbers is greater than either number. Geometry. What is a counterexample of the following conjecture? Conjecture: Any number that is divisible by 3 is also divisible by 6 36 27 23 18 Is it C, 23? A little confused:p Please help? Thanks . mat The process of making conjectures and breaking them with counterexamples is the fundamental way we play with and think about rich tasks, and mathematics as a whole. (Later, when we cannot find counterexamples, we turn to constructing proofs, but that's not where we begin. As an application, we classify compact Sasaki manifolds with non-negative transverse bisectional curvature, which can be viewed as the generalized Frankel conjecture (N. Mok's theorem) in Sasaki geometry. Subjects: Differential Geometry (math.DG) Cite as: arXiv:1209.4026 [math.DG

Mathematicians prove the Umbral Moonshine Conjecture. In theoretical math, the term moonshine refers to an idea so seemingly impossible that it seems like lunacy. Monstrous moonshine, a quirky. Thus The Weil Conjectures―an elegant blend of biography and memoir and a meditation on the creative life. Personal, revealing, and approachable, The Weil Conjectures eloquently explores math as it relates to intellectual history, and shows how sometimes the most inexplicable pursuits turn out to be the most rewarding The Ramanujan Machine is a novel way to do mathematics by harnessing your computer power to make new discoveries. The Ramanujan Machine already discovered dozens of new conjectures. Our algorithms search for new mathematical formulas. The community can suggest proofs for the conjectures or even propose or develop new algorithms

### What is the Tate conjecture? - lcc

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