Vocabulary

  • think of: To look on as (being something specific); consider
  • think about: To consider something carefully.
  • point at: To aim (gun, etc.) at someone or something
  • in fact: Used to emphasize the truth of a statement, especially one that contrasts with or contradicts something else.
  • for example: As an illustration or instance.
  • in general: Typically; usually; on the whole.
  • in terms of
  • to the point: Expressing something directly and without unnecessary detail.
  • walk around: To stroll or wander in a leisurely way.
  • go ahead: To start an activity; start doing, working etc.
  • on the square: Behaving honestly and fairly.
  • dream up: To invent or imagine something, especially something unusual or ingenious.
  • over to: Used to hand over to someone else to speak
  • breaks down: To forcibly break, destroy or make collapse
  • as well as: Also; in addition to
  • zero in: To focus on a target
  • to the day: Exactly on the date specified, without any difference.
  • of sorts: Of a kind, but not a very good one.
  • improve on: To make something better than it was before.
  • for one thing: Used to introduce a reason for something.
  • put out: To publish, e.g. a book
  • take on: To acquire a new characteristic
  • help out: To assist someone
  • stick on: To attach something to a surface using glue or adhesive.
  • for short: As a shortened form of a name or phrase.
  • make up: To invent or create a story
  • consists of: Is made up or composed of.
  • consist of
  • spot on: Exactly right; perfectly accurate.
  • heart and soul: With great enthusiasm and commitment.
  • flip around: To change one's mind or opinion, often suddenly or frequently.
  • third one: The item that is in the third position in a sequence.
  • to the left: In or toward the left direction.
  • feel for: To have sympathy for someone; to empathize with someone's situation.
  • for instance: As an example.
  • name for: To give someone or something a particular name, often in honor of someone else.
  • in a row: One after another without a break.
  • on the real: Honestly or truly; speaking sincerely.
  • break down: To forcibly break, destroy or make collapse
  • by itself: Alone; without help or assistance.
  • think back: To recapture the past
  • spit out: To eject something from the mouth.
  • take in: To allow to enter; receive as a guest
  • plug in
  • to do with: To be about something; concern
  • turn off
  • reach out: To attempt to communicate with someone.
  • instead of: When one thing is replaced by another
  • specific: Precise; particular; just about that thing
  • stretch: To make your arm, leg muscles long to ease them
  • positive: Showing agreement or support for something
  • structure: The way in which the parts of a system or object are arranged or organized, or a system arranged in this way
  • flip: To turn your body in the air, as in gymnastics
  • negative: The opposite to a positive electrical charge
  • associate: Partner in professional work, e.g. in law
  • completely: In every way or as much as possible
  • general: Widespread, normal or usual
  • spot: A certain place or area
  • sense: Certain mental feeling or emotion
  • complex: Group of buildings all used for the same purpose
  • unique: Unlike other things; being the only one like it
  • imagine: To think creatively about; form mental picture of
  • research: To study in order to discover new ideas and facts
  • property: Particular quality that someone or something has
  • theory: Ideas or principles that explain facts or events
  • function: Social event, or party such as a wedding
  • mean: Average of a set of numbers
  • ordinary: Normal or usual
  • association: Organization of people with the same interest
  • formula: A mathematical or scientific rule
  • define: To explain the meaning of words
  • effect: An advantage, benefit
  • apply: To spread a substance or liquid over a surface
  • infinite: Being very large in amount
  • break: To create a new record e.g. running the 100m dash
  • notice: To become aware by sight, touch, or hearing
  • place: To put someone in a particular type of situation
  • important: Having power or authority
  • single: One run in cricket or a hit baseball
  • kind: In a caring and helpful manner
  • fact: Something that is known or proved to be true
  • vertical: (Of a line, etc.) going up and down; not horizontal
  • build: Your physical shape; physique
  • multiply: To increase in number by reproducing/having babies
  • exponential: (Of an increase) at a faster and faster rate
  • symmetry: Having parts that are exactly the same
  • rotation: Regular change of the crops grown in a field
  • evenly: Equally; with advantage to both sides
  • correspond: To have similarity or equality with something
  • squish: To walk through mud or puddles
  • cylinder: Tube shape with flat ends
  • rotate: To regularly change people who perform a role
  • unit: One apartment in a building
  • lab: Short for 'laboratory'
  • arithmetic: Math of adding, subtracting, dividing, multiplying
  • additive: Substance added to a food or drink
  • radius: Area around a certain point
  • emerald: Green-colored gemstone
  • multiplication: Increase in the number of something
  • calculus: Branch of math dealing with rates of change, etc.
  • diagonal: Joining two opposite corners at an angle
  • symmetric: Having parts that are exactly the same
  • pi: The ratio of the circumference to the diameter
  • multiplicative: Having the power to increase in number/degree
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  • not found vocabularyNo vocabulary matches your filters
    • additive

      US /ˈædɪtɪv/

      UK /ˈædətɪv/

      • Noun (Countable/Uncountable)
      • Substance added to a food or drink
      • Adjective
      • Added to a food or drink
      • Relating to or involving addition.
      B1TOEIC
      More
    • arithmetic

      US /əˈrɪθmɪtɪk/

      UK /əˈrɪθmətɪk/

      • Uncountable Noun
      • Math of adding, subtracting, dividing, multiplying
      B2
      More
    • as well as

      US /æz wɛl æz/

      UK /æz wel æz/

      • Adverb
      • Also; in addition to
      • Preposition
      • In addition to; and also.
      A1
      More
    • associate

      US /əˈsoʊʃiˌeɪt/

      UK /ə'səʊʃɪeɪt/

      • Countable Noun
      • Partner in professional work, e.g. in law
      • Verb (Transitive/Intransitive)
      • To spend time with other people; mix with
      • To form a connection in your mind between things
      B1TOEIC
      More
    • association

      US /əˌsoʊʃi'eɪʃn/

      UK /əˌsəʊʃɪ'eɪʃn/

      • Noun
      • Organization of people with the same interest
      B1TOEIC
      More
    • break down

      US /brek daʊn/

      UK /breik daun/

      • Phrasal Verb
      • To forcibly break, destroy or make collapse
      • (Machine) to stop working or become weaker
      A1
      More
    • breaks down

      US

      UK

      • Phrasal Verb
      • To forcibly break, destroy or make collapse
      • (Machine) to stop working or become weaker
      A1
      More
    • by itself

      US /baɪ ɪtˈsɛlf/

      UK /bai itˈself/

      • Adverb
      • Alone; without help or assistance.
      • Without any external influence or aid.
      A2
      More
    • calculus

      US /ˈkælkjələs/

      UK /ˈkælkjələs/

      • Uncountable Noun
      • Branch of math dealing with rates of change, etc.
      C1
      More
    • complex

      US /kəmˈplɛks, ˈkɑmˌplɛks/

      UK /'kɒmpleks/

      • Countable Noun
      • Group of buildings all used for the same purpose
      • Adjective
      • Not being simple; having many parts or aspects
      A2
      More
    • consist of

      US /kənˈsɪst ʌv/

      UK /kənˈsist ɔv/

      • Phrasal Verb
      A2
      More
    • consists of

      US

      UK

      • Phrasal Verb
      • Is made up or composed of.
      A1
      More
    • correspond

      US /ˌkɔ:rəˈspɑ:nd/

      UK /ˌkɒrəˈspɒnd/

      • Intransitive Verb
      • To have similarity or equality with something
      • To write letters or emails to someone
      B1
      More
    • cylinder

      US /ˈsɪləndɚ/

      UK /ˈsɪlɪndə(r)/

      • Noun
      • Tube shape with flat ends
      • A solid geometric figure with straight parallel sides and a circular or oval section.
      B2
      More
    • define

      US /dɪˈfaɪn/

      UK /dɪ'faɪn/

      • Transitive Verb
      • To explain the meaning of words
      • To set or mark the limits of something
      A2TOEIC
      More
    • diagonal

      US /daɪˈæɡənəl/

      UK /daɪˈægənl/

      • Adjective
      • Joining two opposite corners at an angle
      • Noun
      • A straight line joining two opposite corners of a square, rectangle, or other straight-sided shape.
      • A diagonal pattern or design.
      B2
      More
    • dream up

      US /drim ʌp/

      UK /dri:m ʌp/

      • Phrasal Verb
      • To invent or imagine something, especially something unusual or ingenious.
      A1
      More
    • emerald

      US /ˈɛmərəld, ˈɛmrəld/

      UK /ˈemərəld/

      • Noun
      • Green-colored gemstone
      B2
      More
    • evenly

      US /ˈivənlɪ/

      UK /ˈi:vnli/

      • Adverb
      • Equally; with advantage to both sides
      • In a smooth, level or regular way
      B2
      More
    • exponential

      US /ˌɛkspəˈnɛnʃəl/

      UK /ˌekspəˈnenʃl/

      • Adjective
      • (Of an increase) at a faster and faster rate
      C1
      More
    • feel for

      US /fil fɔr/

      UK /fi:l fɔ:/

      • Phrasal Verb
      • To have sympathy for someone; to empathize with someone's situation.
      • To try to find something by touching it.
      A1
      More
    • flip

      US /flɪp/

      UK /flɪp/

      • Verb (Transitive/Intransitive)
      • To turn your body in the air, as in gymnastics
      • To move into a different position quickly
      • Noun
      • Act of turning your body in the air; somersault
      • Movement of something from one position to another
      B2
      More
    • flip around

      US

      UK

      • Phrasal Verb
      • To change one's mind or opinion, often suddenly or frequently.
      • To turn something over quickly, rotating it.
      A2
      More
    • for example

      US

      UK

      • Phrase
      • As an illustration or instance.
      More
    • for instance

      US /fɔr ˈɪnstəns/

      UK /fɔ: ˈinstəns/

      • Adverb
      • As an example.
      • Phrase
      • As an example.
      • As an illustration or case in point
      B1
      More
    • for one thing

      US /fɔr wʌn θɪŋ/

      UK /fɔ: wʌn θiŋ/

      • Phrase
      • Used to introduce a reason for something.
      A1
      More
    • for short

      US /fɔr ʃɔrt/

      UK /fɔ: ʃɔ:t/

      • Phrase
      • As a shortened form of a name or phrase.
      A1
      More
    • formula

      US /ˈfɔrmjələ/

      UK /'fɔ:mjələ/

      • Noun (Countable/Uncountable)
      • A mathematical or scientific rule
      • Plan, rule or method for doing or making something
      A2TOEIC
      More
    • function

      US /ˈfʌŋkʃən/

      UK /'fʌŋkʃn/

      • Noun
      • Social event, or party such as a wedding
      • Mathematical operation used in calculations
      • Intransitive Verb
      • To serve a certain purpose or role
      • To be operating, working or achieving its purpose
      A2TOEIC
      More
    • go ahead

      US /ɡo əˈhɛd/

      UK /ɡəu əˈhed/

      • Phrasal Verb
      • To start an activity; start doing, working etc.
      • To give permission to do something
      • Intransitive Verb
      • To start or proceed with something
      • To proceed despite potential obstacles or doubts.
      A1
      More
    • heart and soul

      US /hɑrt ənd sol/

      UK /hɑ:t ænd səul/

      • Phrase
      • With great enthusiasm and commitment.
      • Noun (Countable/Uncountable)
      • The most important or essential part of something.
      A2
      More
    • help out

      US /hɛlp aʊt/

      UK /help aut/

      • Phrasal Verb
      • To assist someone
      A1
      More
    • improve on

      US /ɪmˈpruv ɑn/

      UK /imˈpru:v ɒn/

      • other
      • To make something better than it was before.
      B1
      More
    • in a row

      US /ɪn e ro/

      UK /in ə rəu/

      • Phrase
      • One after another without a break.
      • Arranged in a straight line.
      • Idiom
      • To have an argument.
      A1
      More
    • in fact

      US /ɪn fækt/

      UK /in fækt/

      • Adverb
      • Used to emphasize the truth of a statement, especially one that contrasts with or contradicts something else.
      • Used to introduce a more detailed or surprising piece of information.
      • Phrase
      • Used to emphasize the truth of a statement, especially one that is surprising or contrary to what might be expected.
      C1
      More
    • in general

      US /ɪn ˈdʒɛnərəl/

      UK /in ˈdʒenərəl/

      • Phrase
      • Typically; usually; on the whole.
      • Not specific or detailed; broadly.
      • Adjective
      • Not detailed or specific; overall.
      C2
      More
    • in terms of

      US

      UK

      • Phrase
      • With regard to; concerning a particular aspect.
      A1
      More
    • infinite

      US /ˈɪnfənɪt/

      UK /'ɪnfɪnət/

      • Adjective
      • Being very large in amount
      • Without an end; limitless; endless
      B2
      More
    • instead of

      US /ɪnˈstɛd ʌv/

      UK /inˈsted ɔv/

      • Preposition
      • When one thing is replaced by another
      • Adverb
      • As a substitute or alternative.
      A1
      More
    • lab

      US /læb/

      UK /læb/

      • Noun (Countable/Uncountable)
      • Short for 'laboratory'
      B1
      More
    • make up

      US /mek ʌp/

      UK /meik ʌp/

      • Phrasal Verb
      • To invent or create a story
      • To add up to
      • Verb (Transitive/Intransitive)
      • To invent a story, excuse, etc.
      • To compensate for something lost, missed, or deficient.
      A1
      More
    • multiplication

      US /ˌmʌltəplɪˈkeʃən/

      UK /ˌmʌltɪplɪˈkeɪʃn/

      • Uncountable Noun
      • Increase in the number of something
      • Process of multiplying one number by another
      B1
      More
    • multiplicative

      US

      UK

      • Adjective
      • Having the power to increase in number/degree
      C2
      More
    • multiply

      US /ˈmʌltəˌplaɪ/

      UK /ˈmʌltɪplaɪ/

      • Verb (Transitive/Intransitive)
      • To increase in number by reproducing/having babies
      • To increase something by a large quantity
      B1
      More
    • name for

      US

      UK

      • Phrasal Verb
      • To give someone or something a particular name, often in honor of someone else.
      A1
      More
    • negative

      US /ˈnɛɡətɪv/

      UK /'neɡətɪv/

      • Noun
      • The opposite to a positive electrical charge
      • In grammar, containing words such as 'no' or 'not'
      • Adjective
      • Being harmful, unwanted or unhelpful
      • In mathematics, being less than zero
      A2
      More
    • of sorts

      US

      UK

      • Phrase
      • Of a kind, but not a very good one.
      • Used to describe something when you cannot be more precise.
      A1
      More
    • on the real

      US /ɑn ðə ˈril/

      UK /ɒn ðə ˈri:əl/

      • other
      • Honestly or truly; speaking sincerely.
      B2
      More
    • on the square

      US /ɑn ðə skwɛɚ/

      UK /ɒn ðə skweə/

      • other
      • Behaving honestly and fairly.
      B2
      More
    • ordinary

      US /ˈɔ:rdneri/

      UK /'ɔ:dnrɪ/

      • Adjective
      • Normal or usual
      • Of the rank of ordinary seaman.
      • Noun
      • An ecclesiastical judge or official having ordinary jurisdiction in a given area.
      • Any of several simple and basic geometrical figures.
      A2TOEIC
      More
    • over to

      US

      UK

      • Preposition
      • Used to hand over to someone else to speak
      • The responsibility is now yours
      More
    • pi

      US /paɪ/

      UK /paɪ/

      • Noun
      • The ratio of the circumference to the diameter
      B2
      More
    • plug in

      US /plʌɡ ɪn/

      UK /plʌɡ in/

      • Phrase
      B1
      More
    • point at

      US

      UK

      • Phrasal Verb
      • To aim (gun, etc.) at someone or something
      A1
      More
    • positive

      US /ˈpɑzɪtɪv/

      UK /ˈpɒzətɪv/

      • Adjective
      • Showing agreement or support for something
      • Being sure about something; knowing the truth
      • Noun
      • A photograph in which light areas are light and dark areas are dark
      A2
      More
    • property

      US /ˈprɑpəti/

      UK /'prɒpətɪ/

      • Noun (Countable/Uncountable)
      • Particular quality that someone or something has
      • Buildings or piece of land owned by someone
      A2TOEIC
      More
    • put out

      US /pʊt aʊt/

      UK /put aut/

      • Phrasal Verb
      • To publish, e.g. a book
      • To cause someone to be troubled or inconvenienced
      A1
      More
    • radius

      US /ˈrediəs/

      UK /ˈreɪdiəs/

      • Noun (Countable/Uncountable)
      • Area around a certain point
      • Countable Noun
      • Long bone on the thumb side of your lower arm
      • Line from the center to the edge of a circle
      B2
      More
    • reach out

      US /ritʃ aʊt/

      UK /ri:tʃ aut/

      • Phrasal Verb
      • To attempt to communicate with someone.
      • To offer help and support to someone.
      B1
      More
    • research

      US /rɪˈsɚtʃ, ˈriˌsɚtʃ/

      UK /rɪ'sɜ:tʃ/

      • Verb (Transitive/Intransitive)
      • To study in order to discover new ideas and facts
      • To study the market relating to marketing products and services.
      • Noun (Countable/Uncountable)
      • Study done to discover new ideas and facts
      • A particular area or topic of study.
      A2TOEIC
      More
    • rotate

      US /ˈroʊteɪt/

      UK /rəʊˈteɪt/

      • Verb (Transitive/Intransitive)
      • To regularly change people who perform a role
      • To regularly change the crops that grow in a field
      B2
      More
    • rotation

      US /roʊˈteɪʃn/

      UK /rəʊˈteɪʃn/

      • Uncountable Noun
      • Regular change of the crops grown in a field
      • Group who take turns performing a certain task
      B2
      More
    • specific

      US /spɪˈsɪfɪk/

      UK /spəˈsɪfɪk/

      • Adjective
      • Precise; particular; just about that thing
      • Concerning one particular thing or kind of thing
      A2
      More
    • spit out

      US

      UK

      • Phrasal Verb
      • To eject something from the mouth.
      • To utter words in an angry or aggressive way.
      A1
      More
    • spot

      US /spɑt/

      UK /spɒt/

      • Noun
      • A certain place or area
      • A difficult time; awkward situation
      • Transitive Verb
      • To see someone or something by chance
      A2TOEIC
      More
    • spot on

      US

      UK

      • Adjective
      • Exactly right; perfectly accurate.
      • Adverb
      • Exactly at the expected or scheduled time.
      • Perfect; excellent.
      B1
      More
    • squish

      US /skwɪʃ/

      UK /skwɪʃ/

      • Intransitive Verb
      • To walk through mud or puddles
      C2
      More
    • stick on

      US /stɪk ɑn/

      UK /stik ɔn/

      • Phrasal Verb
      • To attach something to a surface using glue or adhesive.
      • To continue doing something despite difficulties.
      B1
      More
    • stretch

      US /strɛtʃ/

      UK /stretʃ/

      • Verb (Transitive/Intransitive)
      • To make your arm, leg muscles long to ease them
      • To make something bigger by pulling on it
      • Noun
      • Making arm, leg muscles longer to ease them
      • A consecutive row of things
      A2TOEIC
      More
    • structure

      US /ˈstrʌk.tʃɚ/

      UK /ˈstrʌk.tʃə/

      • Noun (Countable/Uncountable)
      • The way in which the parts of a system or object are arranged or organized, or a system arranged in this way
      • A building or other man-made object.
      • Transitive Verb
      • To plan, organize, or arrange the parts of something
      A2TOEIC
      More
    • symmetric

      US /sɪ'metrɪk/

      UK /sɪ'metrɪk/

      • Adjective
      • Having parts that are exactly the same
      B2
      More
    • symmetry

      US /ˈsɪmɪtri/

      UK /ˈsɪmətri/

      • Uncountable Noun
      • Having parts that are exactly the same
      B2TOEIC
      More
    • take in

      US

      UK

      • Phrasal Verb
      • To allow to enter; receive as a guest
      • To include or add
      • Transitive Verb
      • To absorb (liquid).
      • To understand or comprehend something.
      A1
      More
    • take on

      US /tek ɑn/

      UK /teik ɔn/

      • Phrasal Verb
      • To acquire a new characteristic
      • To accept a new responsibility, role
      A1
      More
    • theory

      US /ˈθiəri, ˈθɪri/

      UK /ˈθiəri/

      • Noun (Countable/Uncountable)
      • Ideas or principles that explain facts or events
      • An idea or belief about something
      A2TOEIC
      More
    • think about

      US /θɪŋk əˈbaʊt/

      UK /θiŋk əˈbaut/

      • Phrasal Verb
      • To consider something carefully.
      • To remember or call to mind.
      A1
      More
    • think back

      US /θɪŋk bæk/

      UK /θiŋk bæk/

      • Phrasal Verb
      • To recapture the past
      A1
      More
    • think of

      US /θɪŋk ʌv/

      UK /θiŋk ɔv/

      • Phrasal Verb
      • To look on as (being something specific); consider
      • To consider or remember something.
      • Verb (Transitive/Intransitive)
      • To imagine or call something to mind
      A1
      More
    • third one

      US

      UK

      • Pronoun
      • The item that is in the third position in a sequence.
      • Noun
      • The third option or choice from a set of possibilities.
      A1
      More
    • to do with

      US

      UK

      • Phrasal Verb
      • To be about something; concern
      A1
      More
    • to the day

      US /tu ðə deɪ/

      UK /tu ðə deɪ/

      • other
      • Exactly on the date specified, without any difference.
      B2
      More
    • to the left

      US

      UK

      • Phrase
      • In or toward the left direction.
      • Situated on the left side of.
      More
    • to the point

      US /tu ði pɔɪnt/

      UK /tu: ðə pɔint/

      • Adjective
      • Expressing something directly and without unnecessary detail.
      • Phrase
      • Relevant and pertinent to the matter at hand.
      A2
      More
    • turn off

      US

      UK

      • Phrasal Verb
      • To make someone feel negatively about something
      A1
      More
    • unique

      US /juˈnik/

      UK /jʊ'ni:k/

      • Adjective
      • Unlike other things; being the only one like it
      • Remarkably special or unusual.
      A2TOEIC
      More
    • unit

      US /ˈjunɪt/

      UK /ˈju:nɪt/

      • Countable Noun
      • One apartment in a building
      • Group of people, e.g. soldiers, that work together
      B2TOEIC
      More
    • vertical

      US /ˈvɜ:rtɪkl/

      UK /ˈvɜ:tɪkl/

      • Adjective
      • (Of a line, etc.) going up and down; not horizontal
      • Extending or operating upward from a base.
      • Noun
      • A vertical line or plane.
      • An upright structural member.
      B1
      More
    • walk around

      US

      UK

      • Phrasal Verb
      • To stroll or wander in a leisurely way.
      • To move about in order to inspect something.
      A2
      More
    • zero in

      US /ˈzɪro ɪn/

      UK /ˈziərəu in/

      • Phrasal Verb
      • To focus on a target
      A1
      More
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    01:03

    She took a brave step forward, leaving behind her comfort zone to chase her dreams.

    Vocabulary
    • brave

      adj. Having courage

    • comfort zone

      phr. A familiar situation where one feels safe

    Explanation
    a brave step is a noun phrase, where brave is an adjective modifying the noun step, meaning "a courageous step". forward is an adverb modifying step, meaning "ahead". The whole phrase serves as the object, answering the "what" of took (verb) — she took a brave step forward.

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    brave

    US/brev/
    UK/breɪv/
    adj.Brave
    v.t.To bravely face
    A2 Elementary

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    Euler's formula with introductory group theory

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    蘿蔔 posted on 2025/01/10
    Ever wondered how Euler's formula connects to group theory? This video dives deep into complex numbers and the exponential function, offering a fantastic visual intuition for math enthusiasts. You'll pick up advanced vocabulary and complex sentence structures while exploring the fascinating Dihedral Group!

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